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

Judith McQueen

Judith McQueen

Answered question

2022-01-07

Evaluate the following indefinite integral.
cos4(x)sin(x)dx

Answer & Explanation

macalpinee3

macalpinee3

Beginner2022-01-08Added 29 answers

Step 1
For a step-by-step explanation of how to find the given integral, see the attached file.
Step 2
Solution cos4(x)sin(x) dx 
(cos(x))4sin(x) dx 
Let cos(x)=t
differentiate sin(x) dx = dt 
sin(x) dx = dt 
t4( dt )
t4 dt 
t55+c
put t=cos(x)
cos5x5+c or (cosx)55+c

Jenny Sheppard

Jenny Sheppard

Beginner2022-01-09Added 35 answers

(sin(x))dx=d(cos(x)),t=cos(x)
(t4)dt
This is a tabular integral:
t4dt=t55+C
To write down the final answer, it remains to substitute cos(x) instead of t.
Result:
cos(x)55+C
karton

karton

Expert2022-01-11Added 613 answers

We have:cos(x)4sin(x)dxt4dtt4dtEvaluatet55cos(x)55Answer:cos(x)55+C

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