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Question
Integrate the functions:
`(x^3 sin(tan^(-1) x^4))/(1 + x^8)`
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Solution
Let `I = int (x^3 sin (tan^-1 x^4))/(1 + x^8)` dx
Put tan-1 x4 = t
or `1/(1 + x^8) * 4x^3 dx = dt`
`1/(1 + x^8). x^3 = 1/4 dt`
Hence, `I = 1/4 int sin t dt`
`= - 1/4 cos t + C`
`= - 1/4 cos (tan^-1 x^4) + C`
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