What is the integral of ((2x+5))/(sqrt(x^2+5x)) ?

The integral of ((2x+5))/(sqrt(x^2+5x)) is 2sqrt(x^2+5x)+C

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integral of ((2x+5))/(sqrt(x^2+5x))

\int \frac{( 2 x + 5 )}{x ^{2} + 5 x} d x

2 x^{2} + 5 x + C

Solution steps

\int \frac{2 x + 5}{x ^{2} + 5 x} d x

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= 2 u^{\frac{1}{2}}

Substitute back

u = x^{2} + 5 x

= 2 (x^{2} + 5 x)^{\frac{1}{2}}

Apply radical rule:

= 2 x^{2} + 5 x

Add a constant to the solution

= 2 x^{2} + 5 x + C

\frac{\partial}{\partial x} (x (e^{y} + e^{y} y))

\frac{d}{d x} (\frac{csc ( x ) tan ( x )}{cos ( x )})

\int sin^{4} (x) \cdot cos (x) d x

x, x, [0, 2]

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What is the integral of ((2x+5))/(sqrt(x^2+5x)) ?
The integral of ((2x+5))/(sqrt(x^2+5x)) is 2sqrt(x^2+5x)+C