What is the integral of x/(sqrt(x^2+81)) ?

The integral of x/(sqrt(x^2+81)) is sqrt(x^2+81)+C

Popular >

integral of x/(sqrt(x^2+81))

\int \frac{x}{x ^{2} + 81} d x

x^{2} + 81 + C

Solution steps

\int \frac{x}{x ^{2} + 81} 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} + 81

= \frac{1}{2} \cdot 2 (x^{2} + 81)^{\frac{1}{2}}

Simplify

\frac{1}{2} \cdot 2 (x^{2} + 81)^{\frac{1}{2}} : x^{2} + 81

= x^{2} + 81

Add a constant to the solution

= x^{2} + 81 + C

\int_{- π}^{π} x^{2} sin (n x) d x

\int \frac{ln ( x ^{28} )}{x} d x

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

\frac{\partial}{\partial x} (4 x (x^{2} + y^{2}) - 4 a^{2} x)

\frac{a}{x}

What is the integral of x/(sqrt(x^2+81)) ?
The integral of x/(sqrt(x^2+81)) is sqrt(x^2+81)+C