What is the integral from 1 to 4 of (3x+5)/(sqrt(x)) ?

The integral from 1 to 4 of (3x+5)/(sqrt(x)) is 24

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integral from 1 to 4 of (3x+5)/(sqrt(x))

\int_{1}^{4} \frac{3 x + 5}{x} d x

24

Solution steps

\int_{1}^{4} \frac{3 x + 5}{x} d x

Apply Integration By Parts

: [2 x (3 x + 5) - \int 6 x d x]_{1}^{4}

= [2 x (3 x + 5) - \int 6 x d x]_{1}^{4}

\int 6 x d x = 4 x^{\frac{3}{2}}

= [2 x (3 x + 5) - 4 x^{\frac{3}{2}}]_{1}^{4}

Compute the boundaries:

24

= 24

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What is the integral from 1 to 4 of (3x+5)/(sqrt(x)) ?
The integral from 1 to 4 of (3x+5)/(sqrt(x)) is 24