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

The integral of (sin(x))/(7+cos(x)) is -ln|7+cos(x)|+C

Popular >

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

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

- ln ∣ 7 + cos (x) ∣ + C

Solution steps

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

Apply u-substitution

: \int - \frac{1}{u} d u

= \int - \frac{1}{u} d u

Take the constant out:

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

= - \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

Substitute back

u = 7 + cos (x)

= - ln ∣ 7 + cos (x) ∣

Add a constant to the solution

= - ln ∣ 7 + cos (x) ∣ + C

\frac{\partial}{\partial x} (y ln (x^{3} + y^{3} + 8) - 7)

\int y^{2} + 1 d y

\frac{d}{d x} ((5 + 3 x) cos (x))

\int_{0}^{1} \frac{x ^{3}}{x ^{2} + 2 x + 1} d x

f (x) = - \frac{12}{x ^{5}}

What is the integral of (sin(x))/(7+cos(x)) ?
The integral of (sin(x))/(7+cos(x)) is -ln|7+cos(x)|+C