Use U-Substitution to evaluate the Integral:

Question

anonymous · Answer

u=(x^{4} + 3x^{2} +5)

anonymous · Answer

$$\int\limits_{?}^{?} (4x^{3} +6x) \cos (x^{4} + 3x^{2} + 5 ) dx$$

anonymous · Answer

I have to integrate that above this post with the U given in the first post.
Please confirm my answer if you can!!

anonymous · Answer

Actually I couldn't get an answer - please helpz!!!

anonymous · Answer

= sin ( u ) = sin ( x^4 + 3x^3 + 5) + C

anonymous · Answer

sorry the second x should be squared ( 3x^2)

anonymous · Answer

because u = x^4 + 3x^3 + 5 ==> du/dx = 4x^3 + 6x solve for dx and plug the equation for dx into the integral

anonymous · Answer

if you write that out you will notice you have 4x^3 + 6x in the numerator and denominator and that equals 1. but you are still multiplying by du. because you had to solve for dx

anonymous · Answer

you get $$\int\limits_{?}^{?}\cos u du$$ = sin u then just plug u back into the sing

anonymous · Answer

taking a step back when you solve for dx you should get 

dx = du / (4x^3 + 6x)

plug that into the integral. you are integrating du with respect to u

anonymous · Answer

$$\sin(x^{4} + 3x^{2} + 5) + c $$

anonymous · Answer

perfect

anonymous · Answer

awesome!! thank you so much!!

anonymous · Answer

yeahp!