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

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

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

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

ln ∣ 7 + sin (x) ∣ + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = 7 + sin (x)

= ln ∣ 7 + sin (x) ∣

Add a constant to the solution

= ln ∣ 7 + sin (x) ∣ + C

\int_{- 6}^{6} 3 t + 4 e^{2 t} - e^{t} d t

\frac{\partial}{\partial y} (x yz + sin (2 x y))

5 cos (π x), 12 x^{3} - 3, 0.5, - 0.5

\frac{1}{1 + x}, 1

f (x) = x^{3} - 6 x, g (x) = - 2 x

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