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    Can someone help me with this question:

    \displaystyle\int^1_0 x^{3} tan^{-1}\left( \dfrac{1-x}{1+x}\right) dx

    I have tried a couple of substitutions including cosx and tan^2x, but none of these have been successful. A hint in the right direction would be appreciated. Thanks .
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    (Original post by brittanna)
    Can someone help me with this question:

    \displaystyle\int^1_0 x^{3} tan^{-1}\left( \dfrac{1-x}{1+x}\right) dx

    I have tried a couple of substitutions including a half angle trig function and tan^2x, but none of these have been successful. A hint in the right direction would be appreciated. Thanks .
    Integration by parts works. Choose u as the arctan.
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    (Original post by brittanna)
    Can someone help me with this question:

    \displaystyle\int^1_0 x^{3} tan^{-1}\left( \dfrac{1-x}{1+x}\right) dx

    I have tried a couple of substitutions including cosx and tan^2x, but none of these have been successful. A hint in the right direction would be appreciated. Thanks .
    you can split the term in the arctan into an expression with no variables on the numerator, and then you can approach it using standard integration by parts and implicit differentiation
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    (Original post by Mr M)
    Integration by parts works. Choose u as the arctan.
    Thank you.
 
 
 
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