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 Notation

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}

= [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}

\int_{0}^{1} \frac{4 x e ^{x}}{3} d x

\int_{1}^{4} (x ln (2) - \frac{3}{2 x}) d x

\int_{0}^{x^{2}} 10 y d y

\int_{0}^{3} y d y

\int_{8}^{27} \frac{1}{x - x ^{\frac{1}{3}}} d x

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