Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Integrals
0 votes

$\Large \int\frac{x^3}{x+1}$ is equal to\begin{array}{1 1}(A)\;x+\frac{x^2}{2}+\frac{x^3}{3}-log\mid1-x\mid+C & (B)\;x+\frac{x^2}{2}-\frac{x^3}{3}-log\mid1-x\mid+C\\(C)\;x-\frac{x^2}{2}-\frac{x^3}{3}-log\mid1+x \mid+C & (D)\;x-\frac{x^2}{2}+\frac{x^3}{3}-log\mid1+x \mid+C\end{array}

Can you answer this question?

1 Answer

0 votes
  • If the degree of the numerator in a rational expression is greater than the denominator,then it is an improper fraction.
  • $\int x^ndx=\large\frac{x^{n+1}}{n+1}$+c.
  • $\int \large\frac{dx}{x+a}=\normalsize \log\mid x+a\mid +c.$
Step 1:
$\large\frac{x^3}{x+1}$ is an improper rational expression,to make proper let us divide
$\int\large \frac{x^3}{x+1}$=$\int (x^2-x+1)dx-\int \large\frac{1}{x+1}\normalsize dx.$
Step 2:
On integrating we get,
$\large\frac{x^3}{3}-\frac{x^2}{2}$+$x-\log\mid x+1\mid+c.$
Correct answer is D.
answered Apr 24, 2013 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App