Toolbox: $\int \sqrt{a^2-x^2}dx=\frac{x}{2}\sqrt{a^2-x^2}+\frac {a^2}{2}\sin^{-1}(\frac{x}...

Toolbox: $\int \sqrt{x^2-a^2}dx=\frac{x}{2}\sqrt{x^2-a^2}+\frac {a^2}{2}log|x+\sqrt{x^2-a^2}|+c$ ...

Toolbox: $\int \sqrt{x^2+a^2}dx=\frac{x}{2}\sqrt{x^2+a^2}+\frac {a^2}{2}log|x+\sqrt{x^2+a^...

Toolbox: $\int \sqrt{a^2-x^2}dx=\frac{x}{2}\sqrt {a^2-x^2}+\frac{a^2}{2}\sin{-1}(\frac{x}{...

Toolbox: $I=\int \sqrt {a^2-x^2} dx=\frac {x}{2}\sqrt{a^2-x^2}+\frac{a^2}{2} \sin {-1}(\fr...

Toolbox: (i) $\int e^x[f(x)+f'(x)]dx=e^x(f(x))+c$ (ii) $ \frac{d}{dx}(\sec x)=\sec x...

Toolbox: (i)Method of substitution: Let us consider $\int f(x) dx.$ If we substitude f(x) ...

Toolbox: (i) If there are two functions u and v, such that the integral function is of the...

Toolbox: (i)$ \int e^x[f(x)+f'(x)]dx=e^x f(x)+c$ (ii) $ \frac{d}{dx}(\frac{1}{(x-1)^...

Toolbox: (i)$\int e^x[f(x)+f'(x)dx]=e^xf(x)+c$ (ii)$\frac{d}{dx}(1/x)= -\frac{1}{x^2}$ Given...