Expert Answer to "Evaluate the following integrals. Include absolute values only..."

defazajx

Answered question

2021-10-15

Evaluate the following integrals. Include absolute values only when needed.

\int \frac{x^{2}}{4 x^{3} + 7} d x

insonsipthinye

Skilled2021-10-16Added 83 answers

Given integrals is

\int \frac{x^{2}}{4 x^{3} + 7} d x

Applying u-substitution

u = 4 x^{3} + 7

\Rightarrow d u = 12 x^{2} d x

∴ x^{2} d x = \frac{d u}{12}

So the integral becomes,

\int \frac{d u}{12 u}

= \frac{1}{12} \int \frac{1}{u} d u

= \frac{1}{12} \ln | u |

substituting back

u = 4 x^{3} + 7

= \frac{1}{12} \ln | 4 x^{3} + 7 | + C

is the required value of given integral.

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?