Express the following integrals in terms of gamma function(1) ∫ 𝑑𝑥√1;𝑥410 (2) ∫ √cot 𝜃 𝑑𝜃
Question
Solution 1
To express the given integrals in terms of the gamma function, we will follow these steps:
(1) ∫ 𝑑𝑥√1;𝑥410:
Step 1: Rewrite the integral using the gamma function. ∫ 𝑑𝑥√1;𝑥410 = ∫ 𝑑𝑥 (𝑥^(-1/2)) (𝑥^4)^(-1/10)
Step 2: Simplify the expression. ∫ 𝑑𝑥 (𝑥^(-1/2)) (𝑥^4)^(-1/10) = ∫ 𝑑𝑥 (𝑥^(-1/2 - 4/10))
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(-1/2 - 4/10))
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