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Question

Evaluate: 10 tan 1(3xx313x2)dx

A
3π23log2
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B
3π432log2
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C
7π2+3log2
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D
3π4+32|og2
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Solution

The correct option is B 3π432log2
Let x=tanθ dx=sec2θdθ

At , x=0,θ=0 and at x=1,θ=π4

And, 3xx313x2=3tanθtan3θ13tan2θ=tan3θ

tan1(tan3θ)=3θ

Now the integration becomes:-

π/403θsec2θdθ

Applying integration by parts:-

=[3θtanθ3tanθdθ]π/40

=[3θtanθ3log|secθ|]π/40

=3π43log2

=3π432log2

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