Question

Help please!
Integral problem below.

Answer 1

Find the Indefinite Integral
\[\int\limits_{}^{} x^2(x^3-7)^{17}\]

Answer 2

whoops

Answer 3

let \(u= x^3-7\)

Answer 4

so \[du= 3x^2 dx \]

Answer 5

\[\frac{du}{dx} = 3x^2 => dx= \frac{du}{3x^2}\]

Answer 6

\[\int x^2(u)^{17}* \frac{du}{3x^2} => \frac{1}{3}\int (u)^{17}du => \frac{1}{3}\frac{u^{18}}{18} +C\]

Answer 7

Then sub back in \(u\).

Answer 8

how did you get 1/3?

Answer 9

Cancelling x^2 and 3x^2

Answer 10

\[\frac{x^2}{3x^2} = \frac{1}{3}\]

Answer 11

Ohhh I see, okay that made more sense. that's where I got stuck. Thank you! @Mimi_x3