What is the integral of 1/(4+3x^2) ?

The integral of 1/(4+3x^2) is 1/(2sqrt(3))arctan((sqrt(3))/2 x)+C

Popular >

integral of 1/(4+3x^2)

\int \frac{1}{4 + 3 x ^{2}} d x

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

Solution steps

\int \frac{1}{4 + 3 x ^{2}} d x

Apply Integral Substitution

= \int \frac{1}{2 3 ( 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}{2 3} \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}{2 3} arctan (u)

Substitute back

u = \frac{3}{2} x

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

Add a constant to the solution

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

\int (x + 4) cos (n) π x d x

\int 14 sin^{2} (x) cos^{3} (x) d x

\frac{\partial}{\partial x} (\frac{1}{\frac{1}{x} + \frac{c}{x} + k})

\frac{\partial}{\partial x} (- y (y + sin (x)))

1 - \frac{3 x}{x ^{3} + 27}

What is the integral of 1/(4+3x^2) ?
The integral of 1/(4+3x^2) is 1/(2sqrt(3))arctan((sqrt(3))/2 x)+C