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  • Can someone help me with this, - Integral Calculus - JEE Main-5

Integrate  \int \frac{x^{5}+x^{3}+x}{x^{2}+1}dx

  • Option 1)

    \frac{x^{3}}{3}+\ln \left ( x^{2}+1 \right )+C

  • Option 2)

    \frac{x^{4}}{3}+\ln \left ( x^{2}+1 \right )+C

  • Option 3)

    \frac{x^{4}}{4}+\frac{1}{2}\ln \left ( x^{2}+1 \right )+C

  • Option 4)

    none of these

 

Answers (1)

best_answer

As we learned,

 

Integration by PARTIAL Fraction -

\int \frac{p(x)}{q(x)}dx  form :

Where     \frac{p(x)}{q(x)}=G(x)+\frac{H(x)}{q(x)}

- wherein

Where H(x) is a Polynomial with degree Less than q(x)

 

 

\int \frac{x^{3}\left ( x^{2}+1 \right )}{x^{2}+1}dx+\int \frac{x}{x^{2}+1}dx

\Rightarrow \! \frac{x^{4}}{4}+\frac{1}{2}\ln \left ( x^{2}+1 \right )+C


Option 1)

\frac{x^{3}}{3}+\ln \left ( x^{2}+1 \right )+C

Option 2)

\frac{x^{4}}{3}+\ln \left ( x^{2}+1 \right )+C

Option 3)

\frac{x^{4}}{4}+\frac{1}{2}\ln \left ( x^{2}+1 \right )+C

Option 4)

none of these

Posted by

gaurav

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