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

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

Popular >

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

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

2 ln x + 2 + 1 + C

Solution steps

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

Apply u-substitution

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

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

Apply u-substitution

: \int \frac{2}{v + 1} d v

= \int \frac{2}{v + 1} d v

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int \frac{1}{v + 1} d v

Apply u-substitution

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

= 2 \cdot \int \frac{1}{w} d w

Use the common integral:

\int \frac{1}{w} d w = ln (∣ w ∣)

= 2 ln ∣ w ∣

Substitute back

= 2 ln x + 2 + 1

Add a constant to the solution

= 2 ln x + 2 + 1 + C

\int (2 x^{3} - 2 x^{2} - x - 2) e^{2 x} d x

\int \frac{1}{( x ^{2} + a ) ^{\frac{3}{2}}} d x

\int 4 x^{2} - 4 x + 5 d x

\int \frac{x - 4}{( x - 1 ) ( x ^{2} + x + 1 )} d x

\int (cos (2 x)) e^{s i n (2 x)} d x

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