Question

Integrate the function : $\frac{3x^2}{x^6 +1}$

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Solution:

To integrate the given function convert it in the integrable form

Let

$\int\frac{3x^2}{x^6 +1}dx \\ \\ \int\frac{3x^2}{( {{x}^{3} })^2 +1}dx \\ \\ let \: {x}^{3} = t \\ \\ 3 {x}^{2} dx = dt \\ \\ so \\ \\ \int\frac{1}{ {t}^{2} +1}dt \\ \\ we \: know \: that \: it \: is \: integrate \: as \\ \\ = {tan}^{ - 1} t + c \\ \\ after \: redo \: substitution \\ \\ \int\frac{3x^2}{x^6 +1}dx = {tan}^{ - 1} ({x}^{3}) + c$
Hope it helps you.