Question

O valor da integral indefinida{X^2.cos(2X^3-7)DX é:

A) sen(6x^2-7x)/6+c

B) sen(2x^3-7)/6+c

C) x^3/3 sen(x^4/2-7x)+c

Answer 1

Olá!

$\displaystyle \int x^2 \cdot \cos(2x^3-7) \, \, dx \\\\\\ u=2x^3-7 \\\\du=6x^2 \, dx \\\\ dx=\frac{1}{6x^2} \, du \\\\\\ \int x^2 \cdot \cos u \cdot \frac{1}{6x^2} \, du \\\\\\ \frac{1}{6} \cdot \int \cos u \, du \\\\\\ \frac{1}{6} \cdot \sin u + C \\\\\\ \frac{1}{6} \cdot \sin (2x^3-7) + C \\\\\\ \frac{\sin(2x^3-7)}{6}+C$