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

The integral of 1/(1+sin^2(x)) is 1/(sqrt(2))arctan(sqrt(2)tan(x))+C

Popular >

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

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

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

Solution steps

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

Apply Trigonometric Substitution

: \int \frac{1}{1 + 2 u ^{2}} d u

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

Apply Integral Substitution

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

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}{1 + v ^{2}} d v

Use the common integral:

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

= \frac{1}{2} arctan (v)

Substitute back

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (7 x e^{x^{2}} + y^{2})

\int \frac{23}{( x ^{2} - 1 ) ^{2}} d x

n = 1 \sum \infty \frac{n - 1}{5 n - 1}

(x^{2} + 2 y^{^{'}}) y^{^{''}} + 2 x y^{^{'}} = 0

\frac{d}{d x} (\frac{3 + 8 x}{5 - 6 x})

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