What is the integral of (cos(t))/(5+sin(t)) ?

The integral of (cos(t))/(5+sin(t)) is ln|5+sin(t)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (cos(t))/(5+sin(t))

\int \frac{cos ( t )}{5 + sin ( t )} d t

ln ∣ 5 + sin (t) ∣ + C

Solution steps

\int \frac{cos ( t )}{5 + 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 = 5 + sin (t)

= ln ∣ 5 + sin (t) ∣

Add a constant to the solution

= ln ∣ 5 + sin (t) ∣ + C

\int (2 x + 1) (x^{2} + x + 1) d x

\int sin^{6} (3 x) d x

\frac{d}{d x} (- 8 (x - 3)^{3} + 27)

f (x) = 2 x^{2} - x^{4}, at x = 1

n = 0 \sum \infty (0.9)^{n}

What is the integral of (cos(t))/(5+sin(t)) ?
The integral of (cos(t))/(5+sin(t)) is ln|5+sin(t)|+C