anonymous 5 years ago Use U-Substitution to evaluate the Integral:

1. anonymous

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

2. anonymous

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

3. anonymous

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

4. anonymous

5. anonymous

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

6. anonymous

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

7. anonymous

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

8. anonymous

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

9. anonymous

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

10. anonymous

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

11. anonymous

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

12. anonymous

perfect

13. anonymous

awesome!! thank you so much!!

14. anonymous

yeahp!