Evaluate the following integral: `int_1^5x/(sqrt(2x-1))dx`

Explanation

Let `I =int_{1}^{5} frac{x}{sqrt{2 x-1}} d x`

Let, `2 x-1=t, then 2 d x=d t,`

When, `x to 1 ; t to 1 and x to 5 ; t to 9`

`x=frac{t+1}{2}`

`I=frac{1}{2} int_{1}^{9} frac{t+1}{sqrt{t}} times frac{d t}{2}`

`=frac{1}{4}[frac{2 t^{frac{3}{2}}}{3}+2 sqrt{t}]_{1}^{9}`

`=frac{1}{4}[18+6-frac{2}{3}-2]`


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