Find the indefinite integral: \int (\sin^{3}x)(\cos x)dx

iohanetc

iohanetc

Answered question

2021-11-08

Find the indefinite integral:
(sin3x)(cosx)dx

Answer & Explanation

komunidadO

komunidadO

Skilled2021-11-09Added 86 answers

Step 1
Our Aim is to evaluate the indefinite integral given below:−
I=sin3(x)cos(x)dx...(i)
Step 2
Considering equation−(i), we have:−
I=sin3(x)cos(x)dx
For the integrand sin3(x)cos(x), we will substitute t=sin(x) and dt
=cos(x)dx
=t3dt
Since, we know that the integral of t3 is t44
=t44 + constant.
Substituting back for t=sin(x)
sin3(x)cos(x)dx=sin4(x)4+ constant

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