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integrate the following integral ∫ sin^3(2x +1)dx

 
integrate the following integral
∫ sin^3(2x +1)dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int sin^{3}(2x+1)dx
I = \int sin(2x+1).sin^{2}(2x+1)dx
I = \int sin(2x+1)(1-cos^{2}(2x+1))dx
I = \int sin(2x+1)dx-\int sin(2x+1)cos^{2}(2x+1))dx
I = \frac{-cos(2x+1)}{2}-\int sin(2x+1)cos^{2}(2x+1))dx
I = \frac{-cos(2x+1)}{2}+\int -sin(2x+1)cos^{2}(2x+1))dx
cos(2x+1) = t
-2sin(2x+1)dx = dt
I = \frac{-cos(2x+1)}{2}+\frac{1}{2}\int t^{2}dt
I = \frac{-cos(2x+1)}{2}+\frac{1}{2}.\frac{t^3}{3}+c
I = \frac{-cos(2x+1)}{2}+\frac{cos^3(2x+1)}{6}+c

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