What is the integral of 1/(2x^2+3) ?

The integral of 1/(2x^2+3) is 1/(sqrt(6))arctan(sqrt(2/3)x)+C

Popular >

integral of 1/(2x^2+3)

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

\frac{1}{6} arctan (\frac{2}{3} x) + C

Solution steps

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

Apply Integral Substitution

= \int \frac{1}{6 ( u ^{2} + 1 )} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int \frac{1}{u ^{2} + 1} d u

Use the common integral:

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= \frac{1}{6} arctan (u)

Substitute back

u = \frac{2}{3} x

= \frac{1}{6} arctan (\frac{2}{3} x)

Combine same powers :

\frac{x}{y} = \frac{x}{y}

= \frac{1}{6} arctan (\frac{2}{3} x)

Add a constant to the solution

= \frac{1}{6} arctan (\frac{2}{3} x) + C

f (x) = x^{2} - 6 x + 9, (- 2, 25)

v \to 3 lim (\frac{v + 1 - 2}{v - 3})

x \to 3 lim (\frac{x - 2}{x ^{2} - 9})

\int \frac{1}{x ^{2} + 4 x + 5} d x

f (x) = \frac{9}{x - 3}, at x = 2

What is the integral of 1/(2x^2+3) ?
The integral of 1/(2x^2+3) is 1/(sqrt(6))arctan(sqrt(2/3)x)+C