What is the integral from 1 to 4 of (4+6x)/(sqrt(x)) ?

The integral from 1 to 4 of (4+6x)/(sqrt(x)) is 36

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integral from 1 to 4 of (4+6x)/(sqrt(x))

\int_{1}^{4} \frac{4 + 6 x}{x} d x

36

Solution steps

\int_{1}^{4} \frac{4 + 6 x}{x} d x

Apply Integration By Parts

: [2 x (4 + 6 x) - \int 12 x d x]_{1}^{4}

= [2 x (4 + 6 x) - \int 12 x d x]_{1}^{4}

\int 12 x d x = 8 x^{\frac{3}{2}}

= [2 x (4 + 6 x) - 8 x^{\frac{3}{2}}]_{1}^{4}

Compute the boundaries:

36

= 36

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What is the integral from 1 to 4 of (4+6x)/(sqrt(x)) ?
The integral from 1 to 4 of (4+6x)/(sqrt(x)) is 36