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Question Number 127349 by bemath last updated on 29/Dec/20

∫ (((1−s^2 )^(5/2) )/s^8 ) ds =?

∫(1−s2)5/2s8ds=?

Commented by liberty last updated on 29/Dec/20

waw ... il-mistoqsija tiegħek hija interessanti ħafna

Answered by liberty last updated on 29/Dec/20

I=∫ ((s^5 (s^(−2) −1)^(5/2) )/s^8 ) ds I=∫ s^(−3) (s^(−2) −1)^(5/2) ds let μ = s^(−2) −1 ⇒dμ = −2s^(−3) ds I=−(1/2)∫ μ^(5/2) dμ = −(1/7)μ^(7/2) + c I=−(1/7)(((1−s^2 )/s^2 ))^(7/2) +c = −(((1−s^2 )^(7/2) )/s^7 ) + c

I=∫s5(s−2−1)5/2s8dsI=∫s−3(s−2−1)5/2dsletμ=s−2−1⇒dμ=−2s−3dsI=−12∫μ5/2dμ=−17μ7/2+cI=−17(1−s2s2)7/2+c=−(1−s2)7/2s7+c

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