Question: "Evaluate the integrals. The integrals are listed in..."

Annette Arroyo

Answered question

2021-10-14

Evaluate the integrals. The integrals are listed in random order so you need to decide which integration technique to use.

\int \frac{x^{2}}{(1 + x^{3}} d x}

Tasneem Almond

Skilled2021-10-15Added 91 answers

I = \int \frac{x^{2}}{(1 + x^{3}} d x}

Let

1 + x^{3} = t

3 x^{2} d x = d t

x^{2} d x = \frac{d t}{3}

I = \int \frac{d t}{3 t}

I = \frac{1}{3} \int \frac{d t}{t}

I = \frac{1}{3} \ln | t | + C

I = \frac{1}{3} \ln | 1 + x^{3} | + C

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?