What is the integral from 1 to 4 of (2+5x)/(sqrt(x)) ?

The integral from 1 to 4 of (2+5x)/(sqrt(x)) is 82/3

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integral from 1 to 4 of (2+5x)/(sqrt(x))

\int_{1}^{4} \frac{2 + 5 x}{x} d x

\frac{82}{3}

Decimal

27.33333 \dots

Solution steps

\int_{1}^{4} \frac{2 + 5 x}{x} d x

Apply Integration By Parts

= [2 x (2 + 5 x) - \int 10 x d x]_{1}^{4}

\int 10 x d x = \frac{20}{3} x^{\frac{3}{2}}

= [2 x (2 + 5 x) - \frac{20}{3} x^{\frac{3}{2}}]_{1}^{4}

Compute the boundaries:

\frac{82}{3}

= \frac{82}{3}

What is the integral from 1 to 4 of (2+5x)/(sqrt(x)) ?
The integral from 1 to 4 of (2+5x)/(sqrt(x)) is 82/3