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The integral I=int(sin^(3)thetacos theta...

The integral `I=int(sin^(3)thetacos theta)/((1+sin^(2)theta)^(2))d theta` simplifies to (where, c is the constant of integration)

A

`(1)/(2)ln(sin theta)+(1)/(1+sin^(2)theta)+c`

B

`(1)/(2)ln(1+sin^(2)theta)+(1)/(1+sin^(2)theta)+c`

C

`ln(sin theta)+(1)/(1+sin^(2)theta)+c`

D

`ln(sin^(2)theta+1)+(1)/(sin^(2)theta+2)+c`

Text Solution

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The correct Answer is:
B
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