What is the integral of 1/(1+144x^2) ?

The integral of 1/(1+144x^2) is 1/12 arctan(12x)+C

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integral of 1/(1+144x^2)

\int \frac{1}{1 + 144 x ^{2}} d x

\frac{1}{12} arctan (12 x) + C

Solution steps

\int \frac{1}{1 + 144 x ^{2}} d x

Apply Integral Substitution

= \int \frac{1}{12 ( 1 + u ^{2} )} d u

Take the constant out:

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

= \frac{1}{12} \cdot \int \frac{1}{1 + u ^{2}} d u

Use the common integral:

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

= \frac{1}{12} arctan (u)

Substitute back

u = 12 x

= \frac{1}{12} arctan (12 x)

Add a constant to the solution

= \frac{1}{12} arctan (12 x) + C

\int \frac{sin ( ln ( 4 ) x ^{2} )}{x} d x

\frac{- 4 e ^{(- 2 s)}}{( s ^{2} - 6 s + 8 )}

y^{^{'}} = t y

\frac{d}{d x} (y^{2} sin (x))

\frac{\partial}{\partial x} ((ln (1 + e^{(x)}))^{2})

What is the integral of 1/(1+144x^2) ?
The integral of 1/(1+144x^2) is 1/12 arctan(12x)+C