Question

The question is integrate x^3 sqrt(x^2+1)

Answer 1

Write the integrand like this:
\[\int x \cdot ((x^2+1)-1)\sqrt{x^2+1}\ dx\]
Then let u=x^2+1.

Answer 2

u=x^2+1
du=2xdx
x^2=u-1
du/2=xdx
new integral:

1/2(u-1)sqrt(u)du
=1/2(u-1)(u^1/2)du
distribute and integrate normally

Answer 3

substitute back for u.

Answer 4

dont we need to eliminate x^3?

Answer 5

that's the (u-1) = x^2
the du eliminates the other x because du/2=xdx so that accounts for all 3 x's

Answer 6

(u-1)*du/2=x^3dx

Answer 7

so whats your answer? because the answer here is \[1/5 (x^{2} + 1)^{3/2} - 1/3 (x^{2} + 1)^{3/2} + C\]

Answer 8

did u get this answer?

Answer 9

yes I got this. except double check the answer you're looking at. the first power there should be 5/2 not 3/2 the second one is still 3/2

Answer 10

yes yessss. im sorry typo. so after how did u integrate the rest?