What is the integral of (sin(x))/(7+cos^2(x)) ?

The integral of (sin(x))/(7+cos^2(x)) is -1/(sqrt(7))arctan((cos(x))/(sqrt(7)))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sin(x))/(7+cos^2(x))

\int \frac{sin ( x )}{7 + cos ^{2} ( x )} d x

- \frac{1}{7} arctan (\frac{cos ( x )}{7}) + C

Solution steps

\int \frac{sin ( x )}{7 + cos ^{2} ( x )} d x

Apply u-substitution

: \int - \frac{1}{7 + u ^{2}} d u

= \int - \frac{1}{7 + u ^{2}} d u

Take the constant out:

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

= - \int \frac{1}{7 + u ^{2}} d u

Apply Integral Substitution

= - \int \frac{1}{7 ( 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}{7} \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}{7} arctan (v)

Substitute back

= - \frac{1}{7} arctan (\frac{cos ( x )}{7})

Add a constant to the solution

= - \frac{1}{7} arctan (\frac{cos ( x )}{7}) + C

\frac{d}{d x} (4 x^{4} - 32 x^{3} + 89 x^{2} - 95 x + 29)

x \to - 5 + lim (\frac{x + 4}{x + 5})

\int_{0}^{2} 4 x - 2 x^{2} d x

t + sin (t)

sin (2 t) cos (5 t)

What is the integral of (sin(x))/(7+cos^2(x)) ?
The integral of (sin(x))/(7+cos^2(x)) is -1/(sqrt(7))arctan((cos(x))/(sqrt(7)))+C