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

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 - sin (x)

= - ln ∣ 7 - sin (x) ∣

Add a constant to the solution

= - ln ∣ 7 - sin (x) ∣ + C

\frac{\partial}{\partial x} (x^{6} y - 3 x^{3} y^{2})

\int \frac{1}{9 x ^{2} + 4} d x

(x - 6)^{\frac{8}{9}}

y = \frac{1 - cos ( x )}{sin ( x )}

y^{^{''}} + 16 y^{^{'}} + 64 y = t^{2} e^{- 8 t} - e^{- 8 t}

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