What is the integral of (2x+1)/(sqrt(x^2+x)) ?

The integral of (2x+1)/(sqrt(x^2+x)) is 2sqrt(x^2+x)+C

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integral of (2x+1)/(sqrt(x^2+x))

\int \frac{2 x + 1}{x ^{2} + x} d x

2 x^{2} + x + C

Solution steps

\int \frac{2 x + 1}{x ^{2} + 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} + x

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

Apply radical rule:

a^{\frac{1}{n}} = n a

= 2 x^{2} + x

Add a constant to the solution

= 2 x^{2} + x + C

7 x^{2} + 4

θ \to 0 lim (\frac{sin ( 2 θ )}{θ})

\int \frac{sec ^{2} ( y )}{a + b tan ( y )} d y

(- 6, - 8), (- 14, 4)

\int_{\frac{1}{2}}^{3} \frac{3}{x} - \frac{1}{3} x d x

What is the integral of (2x+1)/(sqrt(x^2+x)) ?
The integral of (2x+1)/(sqrt(x^2+x)) is 2sqrt(x^2+x)+C