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

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

Popular >

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

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

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

Solution steps

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

Apply Trigonometric Substitution

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

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

Apply Integral Substitution

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

Substitute back

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

Add a constant to the solution

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

f (x) = 7 sin (x) + 3 cos (x)

\frac{1}{2 x}

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

\int \frac{( x ^{3} - 1 )}{x ^{2} ( x - 2 ) ^{3}} d x

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

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