Question

Helpppp Please!!!(:
Find the indefinite integrals.
Problems below.

Answer 1

\[\int\limits_{}^{} x^3(3+13x^{4} )^{12}\]

Answer 2

and
\[\int\limits_{}^{} x^2(x^3-7)^{17}\]

Answer 3

Tried a substitution? Notice that the derivative of 3+13x^4 is 4*13x^3...that's a good clue that you should use a substitution.

Answer 4

(since there is an x^4 out front)

Answer 5

how do I do that?

Answer 6

let u= 3+13x^4

Answer 7

Yes. Now find du/dx.

Answer 8

I don't know how to do that?

Answer 9

@Loser66

Answer 10

Differentiate u= 3+13x^4

Answer 11

52x^3

Answer 12

Correct. \[\Large \frac{ du }{dx } = 52x^3\] now rearrange it a bit, to write it this way... (divide both sides by 52, multiply both sides by dx)

\[\Large \frac{ du }{52 } = x^3 dx\]

Answer 13

\[du=\frac{ x^3 dx }{ 52 }\]

Answer 14

remember to include that dx

Answer 15

Keep it as what i wrote, \[\Large \frac{ du }{52 } = x^3 dx\] the reason you do that is because of the original integral... \[\Large \int\limits\limits_{}^{} x^3(3+13x^{4} )^{12} dx\] which we can write as \[\Large \int\limits\limits\limits_{}^{} (3+13x^{4} )^{12} x^3 dx\] now look at this again... \[\Large \frac{ du }{52 } = x^3 dx\]