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

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

Popular >

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

integral

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

x^{2} + 1 + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{2 u} d u

= \int \frac{1}{2 u} d u

Take the constant out:

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

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

Apply the Power Rule

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

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

Substitute back

u = x^{2} + 1

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

Simplify

\frac{1}{2} \cdot 2 (x^{2} + 1)^{\frac{1}{2}} : x^{2} + 1

= x^{2} + 1

Add a constant to the solution

= x^{2} + 1 + C

\int 4 e^{- x} cos (x) d x

\int \frac{3 cos ( x )}{- 2 + 10 sin ( x )} d x

\int e^{- t} \cdot sin (t) d t

\int \frac{ln ^{2} ( x ^{4} )}{x} d x

\int 1.5 d x

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