How to integrate $$\int_0^b x\cdot(a-x)^\frac{1}{7} dx$$ with $a,b,x>0$
How to integrate $\int_0^b x\cdot(a-x)^\frac{1}{7} dx$
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integration
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0u = a - x : x = a - u : dx = - du : then expand it to a polynomial – 2017-01-12
1 Answers
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The substitution $u=a-x$ gives us
$$=-\int_a^{a-b}(a-u)u^{1/7}\ du=\int^a_{a-b}au^{1/7}-u^{8/7}\ du=\left.\frac78au^{8/7}-\frac7{15}u^{15/7}\right|_{a-b}^a$$