Question

Evaluate the indefinite integral:
(x^4)sqrt(12 + x^5)dx

Answer 1

pleaaaaase i neeed the answer !!!!! thanks!!!

Answer 2

integrate x^4 sqrt(12+x^5) dx
For the integrand x^4 sqrt(x^5+12), substitute u = x^5+12 and du = 5 x^4 dx:
= 1/5 integral sqrt(u) du
The integral of sqrt(u) is (2 u^(3/2))/3:
= (2 u^(3/2))/15+constant
Substitute back for u = x^5+12:
= 2/15 (x^5+12)^(3/2)+constant

Answer 3

that's correct, did you understand it Nat? ^_^

Answer 4

\[ \int\limits_{}^{}x^4\sqrt{x^5 + 12}dx\]

take the following:
\[u = x^5 + 12\]
\[du = 5x^4dx\]

now you'll have the following form :
\[=1/5\int\limits_{}^{}\sqrt{u}du\]
\[=1/5[2u^{3/2}/3] + c\]
\[=[ 2(x^5+12)^{3/2}/15] + c\]

just like what elouis has done :) I hope it's clearer now ^_^

Answer 5

thank you so much! that helped a lot!

Answer 6

nvm oops