`int xsqrt(x-5)dx` Find the indefinite integral

Given to solve

`int x(sqrt(x-5))dx`

let `u = x-5`

`du = dx ` and `x= u+5`

so ,

`int x(sqrt(x-5))dx = int (u+5)u^(1/2) du`

=` int [u^(3/2)+5u^(1/2)] du`

= `int u^(3/2) du +int 5u^(1/2) du`

= `(u^((3/2)+1))/((3/2)+1) +5 int u^(1/2) du`

= `u^(5/2)/(5/2) +5 (u^((1/2)+1))/((1/2)+1) + C`

=`u^(5/2)/(5/2) +5 u^(3/2)/(3/2) + C`

=(`2/5)u^(5/2) + (10/3)u^(3/2) + C`

=`2/5(x-5)^(5/2) + 10/3(x-5)^(3/2) + C`

Comments

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