Evaluate the indefinite integral. \int \cos x(3\sin x-1)dx

lugreget9

lugreget9

Answered question

2021-12-30

Evaluate the indefinite integral.
cosx(3sinx1)dx

Answer & Explanation

scomparve5j

scomparve5j

Beginner2021-12-31Added 38 answers

Step 1
Consider the provided integral,
cosx(3sinx1)dx
Evaluate the indefinite integral.
Apply the substitution method,
Let, u=3sinx1du=3cosxdx.
Step 2
Therefore the integral becomes,
cosx(3sinx1)dx=u3du
=13udu
=13u1+11+1+C
=u26+C
Step 3
Substitute back u=3sinx1 in the above integral,
cosx(3sinx1)dx=16(3sin(x)1)2+C
Hence.
Cheryl King

Cheryl King

Beginner2022-01-01Added 36 answers

cos(x)(3sin(x)1)dx
=13udu
udu
=u22
13udu
=u26
=(3sin(x)1)26
cos(x)(3sin(x)1)dx
=(3sin(x)1)26+C
karton

karton

Expert2022-01-04Added 613 answers

cos(x)×(3sin(x)1)dx
Remove the parentheses
3cos(x)sin(x)cos(x)dx
Simplify the expression
32×sin(2x)cos(x)dx
Calculate
3sin(2x)2cos(x)dx
Use properties of integrals
3sin(2x)2dxcos(x)dx
Evaluate the integrals
3cos(2x)4sin(x)
Add C
Solution
3cos(2x)4sin(x)+C

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