What is the integral of (sqrt(x+a))/(x+a) ?

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

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integral of (sqrt(x+a))/(x+a)

\int \frac{x + a}{x + a} d x

2 x + a + C

Solution steps

\int \frac{x + a}{x + a} d x

Simplify

\frac{x + a}{x + a} : \frac{1}{x + a}

= \int \frac{1}{x + a} 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 + a

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

Apply radical rule:

= 2 x + a

Add a constant to the solution

= 2 x + a + C

\int \frac{( 1 + x )}{x} d x

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\int a^{b x} d x

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