What is the integral of (cos(t))/(6+sin(t)) ?

The integral of (cos(t))/(6+sin(t)) is ln|6+sin(t)|+C

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integral of (cos(t))/(6+sin(t))

\int \frac{cos ( t )}{6 + sin ( t )} d t

ln ∣ 6 + sin (t) ∣ + C

Solution steps

\int \frac{cos ( t )}{6 + sin ( t )} d t

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 = 6 + sin (t)

= ln ∣ 6 + sin (t) ∣

Add a constant to the solution

= ln ∣ 6 + sin (t) ∣ + C

\int_{0}^{6} e^{- x^{2}} d x

\int_{0}^{\infty} x^{5} e^{- x} d x

\frac{\partial}{\partial x} (x^{10} + x y^{11} + 9)

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

\frac{d}{d x} (cos^{2} (x^{4}))

What is the integral of (cos(t))/(6+sin(t)) ?
The integral of (cos(t))/(6+sin(t)) is ln|6+sin(t)|+C