Evaluate the following integral. \int x^{3}\sin (x^{4})\cos^{5}(x^{4})dx

zagonek34

zagonek34

Answered question

2021-12-29

Evaluate the following integral.
x3sin(x4)cos5(x4)dx

Answer & Explanation

Joseph Fair

Joseph Fair

Beginner2021-12-30Added 34 answers

Step 1
Consider the given integral
x3sin(x4)cos5(x4)dx
Step 2
Use substitution method to evaluate the integral
Let u=cos(x4)
Then du=4x3sin(x4)dx
x3sin(x4)dx=14du
Step 3
Then the integral becomes
x3sin(x4)cos5(x4)dx=u5(14)du
=14u5du
=14[u66]
=u624
Substituting u=cos(x4), we get cos6(x4)24
x3sin(x4)cos5(x4)dx=cos6(x4)24+C,
where C is the constant of integration.
Heather Fulton

Heather Fulton

Beginner2021-12-31Added 31 answers

x3sin(x4)cos5(x4)dx
4x3dx=d(x4),t=x4
sin(t)cos(t)54dt
(sin(x))dx=d(cos(x)),u=cos(x)
(u54)du
u54du=u624+C
cos(t)624+C
cos(x4)624+C
Vasquez

Vasquez

Expert2022-01-07Added 669 answers

x3sin(x4)cos5(x4)dxTransformt54dt14t5dt14t66Substitute back14cos(x4)66Multiplycos(x4)624Add CSolutioncos(x4)624+C

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?