What is the integral of x/(4+5x^2) ?

The integral of x/(4+5x^2) is 1/10 ln|4+5x^2|+C

Popular >

integral of x/(4+5x^2)

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

\frac{1}{10} ln 4 + 5 x^{2} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{10 u} d u

= \int \frac{1}{10 u} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{10} ln ∣ u ∣

Substitute back

u = 4 + 5 x^{2}

= \frac{1}{10} ln 4 + 5 x^{2}

Add a constant to the solution

= \frac{1}{10} ln 4 + 5 x^{2} + C

\int (\frac{4}{x} + \frac{9}{x ^{7}}) d x

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

\frac{\partial}{\partial x} (1 - y^{2})

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

h \to 0 lim (\frac{( 1 + h ) ^{8} - 1}{h})

What is the integral of x/(4+5x^2) ?
The integral of x/(4+5x^2) is 1/10 ln|4+5x^2|+C