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Answers posted by sreemathi.v

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Integrate the rational functions\[\frac{x^3+x+1}{x^2-1}\]
answered Feb 6, 2013
Toolbox: (i)If the rational is improper in nature we can divide and separate the terms to ...
0 votes
Integrate the rational functions\[\frac{5x}{(x+1)(x^2-4)}\]
answered Feb 6, 2013
Toolbox: $(i)\;$Form of the rational function\[\frac{px+q}{(x+a)(x+b)(x+c)}\] $\;$Fo...
0 votes
Integrate the rational functions\[\frac{2x-3}{(x^2-1)(2x+3)}\]
answered Feb 6, 2013
Toolbox: $(i)\;$Form of the rational function\[\frac{px+q}{(x-a)(x-b)(x-c)}\] $\;$Form of the ...
0 votes
Integrate the rational functions\[\frac{3x+5}{x^3-x^2-x+1}\]
answered Feb 6, 2013
Toolbox: $(i)\;$Form of the rational function\[\frac{px+q}{(x-a)^2(x-b)}\] $\;$Form ...
0 votes
Integrate the rational functions\[\frac{x}{(x-1)^2(x+2)}\]
answered Feb 6, 2013
Toolbox: $(i)\;$Form of the rational function\[\frac{px+q}{(x-a)^2(x-b)}\] $\;$Form ...
0 votes
Integrate the rational functions\[\frac{x}{(x^2+1)(x-1)}\]
answered Feb 5, 2013
Toolbox: $(i)\;$Form of the rational function\[\frac{px+q}{(x+a)(x^2+b)}\] $\;$Form ...
0 votes
Integrate the rational functions $\frac{2x}{x^2+3x+2}$
answered Feb 5, 2013
Toolbox: $(i)\;$Form of the rational function\[\frac{px+q}{(x+a)(x+b)}\] $\;$Form of...
0 votes
Integrate the rational functions\[\frac{x}{(x-1)(x-2)(x-3)}\]
answered Feb 5, 2013
Toolbox: $(i)\;$Form of the rational function\[\frac{px+q}{(x-a)(x-b)(x-c)},a\neq b\neq c\...
0 votes
Integrate the rational functions\[\frac{3x-1}{(x-1)(x-2)(x-3)}\]
answered Feb 5, 2013
Toolbox: $(i)\;$Form of the rational function\[\frac{px+q}{(x-a)(x-b)(x-c)},a\neq b\neq c\...
0 votes
Integrate the rational functions $\frac{1}{x^2-9}$
answered Feb 5, 2013
Toolbox: $(i)\;$Form of the rational function\[\frac{px+q}{(x-a)(x-b)},a\neq b\] $(i...
0 votes
Integrate the rational functions\[\frac{x}{(x+1)(x+2)}\]
answered Feb 5, 2013
Toolbox: $(i)\;$Form of the rational function\[\frac{px+q}{(x-a)(x-b)},a\neq b\] $(i...
0 votes
$\Large \int \normalsize\frac{dx}{\sqrt{9x-4x^2}}$ equals
answered Feb 5, 2013
Toolbox: $\int\frac{dx}{a^2-x^2}=\sin^{-1}\big(\frac{x}{a}\big)+c.$ Given $I=\int\...
0 votes
Choose the correct answer in $\Large \int \normalsize\frac{\large dx}{\large x^2+2x+2}$ equals
answered Feb 5, 2013
Toolbox: $\int\frac{dx}{x^2+a^2}=\frac{1}{a}\tan^{-1}\big(\frac{x}{a}\big)+c.$ Giv...
0 votes
Integrate the functions\[\frac{5x+3}{\sqrt{x^2+4x+10}}\]
answered Feb 5, 2013
Toolbox: $(i)\int\frac{(px+q)}{\sqrt{ax^2+bx+c}}dx.$,where p,q,a,b,c are constants,we are ...
0 votes
Integrate the functions\[\frac{x+3}{x^2-2x-5}\]
answered Feb 5, 2013
Toolbox: $(i)\int\frac{(px+q)}{\sqrt{ax^2+bx+c}}dx.$,where p,q,a,b,c are constants,we are ...
0 votes
Integrate the functions\[\frac{x+2}{\sqrt{x^2+2x+3}}\]
answered Feb 5, 2013
Toolbox: $(i)\int\frac{(px+q)}{\sqrt{ax^2+bx+c}}dx.$,where p,q,a,b,c are constants,we are ...
0 votes
Integrate the functions\[\frac{x+2}{\sqrt{4x-x^2}}\]
answered Feb 4, 2013
Toolbox: $(i)\int\frac{(px+q)}{\sqrt{ax^2+bx+c}}dx.$,where p,q,a,b,c are constants,we are ...
0 votes
Integrate the functions\[\frac{6x+7}{\sqrt{(x-5)(x-4)}}\]
answered Feb 4, 2013
Toolbox: $(i)\int\frac{(px+q)}{\sqrt{ax^2+bx+c}}dx.$,where p,q,a,b,c are constants,we are ...
0 votes
Integrate the functions\[\frac{5x-2}{1+2x+3x^2}\]
answered Feb 4, 2013
Toolbox: $(i)\int\frac{(px+q)}{\sqrt{ax^2+bx+c}}dx.$,where p,q,a,b,c are constants,we are ...
0 votes
Integrate the functions\[\frac{x+2}{\sqrt{x^2-1}}\]
answered Feb 4, 2013
Toolbox: $(i)\int\frac{(px+q)}{\sqrt{ax^2+bx+c}}dx.$,where p,q,a,b,c are constants,we are ...
0 votes
Integrate the functions\[\frac{4x+1}{\sqrt{2x^2+x-3}}\]
answered Feb 4, 2013
Toolbox: $\int\frac{(px+q)}{\sqrt{ax^2+bx+c}}dx.$,where p,q,a,b,c are constants,we are to ...
0 votes
Integrate the functions $\frac{1}{\sqrt{(x-a)(x-b)}}$
answered Feb 4, 2013
Toolbox: $\int\frac{dx}{\sqrt{x^2-a^2}}=log\mid x+\sqrt{x^2-a^2}\mid+c.$ Given:$I=...
0 votes
Integrate the functions\[\frac{1}{\sqrt{8+3x-x^2}}\]
answered Feb 4, 2013
Toolbox: $\int\frac{dx}{\sqrt{a^2-x^2}}=\sin^{-1}\big(\frac{x}{a}\big)+c.$ Given:$...
0 votes
Integrate the functions\[\frac{1}{\sqrt{(x-1)(x-2)}}\]
answered Feb 4, 2013
Toolbox: $\int\frac{dx}{\sqrt{x^2-a^2}}=log\mid x+\sqrt{x^2-a^2}\mid+c.$ Given:$I=...
0 votes
Integrate the functions\[\frac{1}{\sqrt{7-6x-x^2}}\]
answered Feb 4, 2013
Toolbox: $\int\frac{dx}{\sqrt{a^2-x^2}}=\sin^{-1}\big(\frac{x}{a}\big)+c.$ Given $...
0 votes
Integrate the functions\[\frac{1}{9x^2+6x+5}\]
answered Feb 4, 2013
Toolbox: $\int\frac{dx}{x^2+a^2}=\frac{1}{a}\tan^{-1}\big(\frac{x}{a}\big)+c.$ Giv...
0 votes
Integrate the functions\[\frac{1}{\sqrt{x^2+2x+2}}\]
answered Feb 4, 2013
Toolbox: $\int\frac{dx}{\sqrt{x^2+a^2}}=\int log\mid x+\sqrt{x^2+a^2}\mid+c.$ Give...
0 votes
Integrate the functions\[\frac{\sec^2x}{\sqrt{\tan^2x+4}}\]
answered Feb 4, 2013
Toolbox: $\int\frac{dx}{\sqrt{x^2+a^2}}=\int log\mid x+\sqrt{x^2+a^2}\mid+c.$ Give...
0 votes
Integrate the functions\[\frac{x^2}{\sqrt{x^6+a^6}}\]
answered Feb 4, 2013
Toolbox: $\int\frac{dx}{\sqrt{x^2+a^2}}=\int log\mid x+\sqrt{x^2+a^2}\mid+c.$ Give...
0 votes
Integrate the functions\[\frac{x-1}{\sqrt{x^2-1}}\]
answered Feb 4, 2013
Toolbox: $\int\frac{dx}{\sqrt{x^2-a^2}}=\int log\mid x+\sqrt{x^2-a^2}\mid+c.$ Give...
0 votes
Integrate the functions\[\frac{x^2}{1-x^6}\]
answered Feb 4, 2013
Toolbox: $\int\frac{dx}{\sqrt{a^2+x^2}}=\frac{1}{2a}log\mid\frac{a+x}{a-x}\mid+c.$ ...
0 votes
Integrate the functions\[\frac{3x}{1+2x^4}\]
answered Feb 4, 2013
Toolbox: $\int\frac{dx}{\sqrt{a^2+x^2}}=\frac{1}{a}\tan^{-1}\big(\frac{x}{a}\big)+c.$ ...
0 votes
Integrate the functions $\frac{1}{\sqrt{9-25x^2}}$
answered Feb 4, 2013
Toolbox: $\int\frac{dx}{\sqrt{a^2+x^2}}=\sin^{-1}\big(\frac{x}{a}\big)+c.$ Given:$...
0 votes
Integrate the functions\[\frac{1}{\sqrt{(2-x)^2+1}}\]
answered Feb 4, 2013
Toolbox: $\int\frac{dx}{\sqrt{a^2+x^2}}=log\mid x+\sqrt{x^2+a^2}\mid+c.$ Given:$I=...
0 votes
Integrate the functions\[\frac{1}{\sqrt{1+4x^2}}\]
answered Feb 4, 2013
Toolbox: $\int\frac{dx}{\sqrt{a^2+x^2}}=log\mid x+\sqrt{x^2+a^2}\mid+c.$ Given:$I=...
0 votes
Integrate the functions\[\frac{3x^2}{x^6+1}\]
answered Feb 3, 2013
Toolbox: $(i)\;\int \frac{dx}{x^2+1}=\tan^{-1}x+c.$ Given $I=\int\frac{3x^2}{x^6+1...
0 votes
$\Large \int \normalsize\frac{\large e^x(1+x)}{\large \cos^2(e^xx)}dx$ equals
answered Feb 3, 2013
Toolbox: $(i)\;\int e^{-x}=e^{-x}+c.$ $(ii)\;\int\sec^2xdx=\tan x+c.$ Given ...
0 votes
Choose the correct answer in $\Large \int \normalsize\frac{\large \sin^2x-\cos^2x}{\large \sin^2x\cos^2x}dx$ is equal to
answered Feb 3, 2013
Toolbox: $(i)\;\int \sec^2xdx=\tan x+c.$ $(ii)\;\int cosec^2xdx=-\cot x+c.$ ...
0 votes
Find the integrals of the functions $\frac{1}{\cos(x-a)\cos(x-b)}$
answered Feb 3, 2013
Toolbox: $(i)\;\sin(A+B)=\sin A\cos B+\cos A\sin B.$ $(ii)\;\int\tan xdx=-log|\cos x...
0 votes
Find the integrals of the functions $\sin^{-1}(\cos x)$
answered Feb 3, 2013
Toolbox: $(i)\;\int\frac{1}{\sqrt{1-x^2}dx}=\sin^{-1}x+c.$ $(ii)\;$Method of substit...
0 votes
Find the integrals of the functions $\frac{\cos2x}{(\cos x+\sin x)^2}$
answered Feb 3, 2013
Toolbox: $(i)\;\sin2x=2\sin x\cos x.$ $(ii)\;\int\frac{1}{x}dx=log x+c.$ $(iii...
0 votes
Find the integrals of the function $\frac{1}{\sin x\cos^3x}$
answered Feb 3, 2013
Toolbox: $(i)\;\sin^2x+\cos^2x=1.$ $(ii)\;Method\;of\;substitution.$ Let f(x)=...
0 votes
Find the integrals of the functions $\frac{\cos2x+2\sin^2x}{\cos^2x}$
answered Feb 3, 2013
Toolbox: $(i)\cos2x=1-2\sin^2 x+c.$ $(ii)\;\int \sec^2xdx=\tan x+c$. Given $...
0 votes
Find the integrals of the functions $\frac{\sin^3x+\cos^3x}{\sin^2x\cos^2x}$
answered Feb 3, 2013
Toolbox: $(i)\;\int\sec x\tan xdx=\sec x+c.$ $(ii)\;\int \cot xcosec xdx=-cosec x+c$...
0 votes
Find the integrals of the functions $\tan^4x$
answered Jan 31, 2013
Toolbox: $(i)\tan^2x=\sec^2x-1$ $(ii)\int \sec^2xdx=\tan x+c.$ Given $I=\int...
0 votes
Find the integrals of the functions\[\tan^32x\sec2x\]
answered Jan 31, 2013
Toolbox: $\tan^2x=\sec^2x-1.$ $(ii)\int \sec^2xdx=\tan x+c.$ Given $I=\int\t...
0 votes
Find the integrals of the functions\[\frac{\cos x-\sin x}{1+\sin2x}\]
answered Jan 31, 2013
Toolbox: $(i)\sin^2x+\cos^2x=1.$ $(ii)\sin2x=2\sin x\cos x.$ $(iii)method\;of\...
0 votes
Find the integrals of the functions\[\frac{\cos2x-\cos2\alpha}{\cos x-\cos\alpha}\]
answered Jan 31, 2013
Toolbox: $(i)\cos C-\cos D=-2\sin\frac{(C+D)}{2}\sin\frac{(C-D)}{2}.$ $(ii)\sin x=2\...
0 votes
Find the integrals of the functions $\frac{\sin^2x}{1+\cos x}$
answered Jan 31, 2013
Toolbox: $(i)\sin2x=2\sin x\cos x.$ $\cos x=2\cos^2\frac{x}{2}-1.$ $(iii)\sin ...
0 votes
Find the integrals of the functions\[\cos^42x\]
answered Jan 31, 2013
Toolbox: $(i)\sin^2x=\frac{(1-\cos 2x)}{2}.$ $(ii)\int\cos ^2xdx=\frac{(1+\cos2 x)}{...
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