## anonymous 5 years ago Evaluate the indefinite integral: (x^4)sqrt(12 + x^5)dx

1. anonymous

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

2. anonymous

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

3. anonymous

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

4. anonymous

$\int\limits_{}^{}x^4\sqrt{x^5 + 12}dx$ 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 ^_^

5. anonymous

thank you so much! that helped a lot!

6. anonymous

nvm oops