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Popular >

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

Solution

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

Solution

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

Graph

Popular Examples

integral of 5ln(x^2-x+6)

\int 5 ln (x^{2} - x + 6) d x

integral of e^x+9/x-4

\int e^{x} + \frac{9}{x} - 4 d x

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

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

integral of (a-bx^2)

\int (a - b x^{2}) d x

integral of 0.01x

\int 0.01 x d x

Frequently Asked Questions (FAQ)

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