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

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

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

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

ln ∣ 7 + sin (t) ∣ + C

Solution steps

\int \frac{cos ( t )}{7 + 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 = 7 + sin (t)

= ln ∣ 7 + sin (t) ∣

Add a constant to the solution

= ln ∣ 7 + sin (t) ∣ + C

y = x^{2} + 10 x + 25, y = 7 x + 35

\int \frac{1}{( 1 + x ) ( 1 - x )} d x

\frac{1}{x - 9}

\frac{d}{d x} (\frac{1 - 6 x}{5 + x})

\int \frac{1}{8 - x} d x

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