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How do you integrate #x^3/(1+x^2)#?

Answer 1

Charles Arocha

I found: #1/2[(1+x^2)-ln|1+x^2|]+c#

try this:

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Answer 2

Emma Aldridge

To integrate ( \frac{x^3}{1+x^2} ):

Perform polynomial long division to divide ( x^3 ) by ( 1+x^2 ).
Write ( x^3 ) as ( (1+x^2)(x) - x ).
Integrate both terms separately.
Integrate ( (1+x^2)(x) ) using substitution or the reverse power rule.
Integrate ( -x ) directly.
Combine the results.

The integral of ( \frac{x^3}{1+x^2} ) is ( \frac{1}{2}x^2 - \ln|1+x^2| + C ), where ( C ) is the constant of integration.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.