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I am interested in the evaluation of

$$\int^1_0 \left(1-x^2\right)^{n/2} \sin(kx)\, dx$$

Really $n$ is an odd integer here (the even case is easy).

Ooops, I think the posting

Integral $\int_{-1}^1 \frac{e^x}{\sqrt{1-x^2}}dx$

pretty much covers it, esp. the answer from J.M.

  • 0
    Did yoy try trigonometric substitutions? like $1-x^2 = \cos^2(\theta)$?2012-10-22

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