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Can someone solve this integral question?
y = (x+2)^0.5 (2(x^3))
and
y = (2x-1)^0.5 (x^2+3)^4
I know the answers so please just tell me how to intergrate it
y = (2x-1)^0.5 ((x^2)+3)^4 , question no. 2
1 Answer
- ♣ K-Dub ♣Lv 61 decade agoFavorite Answer
For both, you want to u-substitute so you have sqrt(u). I'll show what you can do with the other part.
First one:
y = (x+2)^0.5 (2(x^3))
Sub: u = x+2, u - 2 = x, du = dx
Integrand becomes:
2 * u^(1/2) * (u - 2)^3.
Now we can expand (u-2)^3 = u^3 - 6u^2 + 12u - 8, then distribute the u^(1/2) (leave the constant multiple 2 outside)
2 * [u^(3+1/2) - 6u^(2+1/2) + 12u^(1+1/2) - 8u^(1/2)].
= 2 * [u^(7/2) - 6u^(5/2) + 12u^(3/2) - 8u^(1/2)].
Now you can integrate term by term.
The second one works similarly. Let u = 2x - 1, (u+1)/2 = x, du/2 = dx. I don't want to do the algebra though.... be careful (looks like torture).
Good luck.
