What is the integral of e^tcot(e^t-8) ?

The integral of e^tcot(e^t-8) is ln|sin(e^t-8)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^tcot(e^t-8)

\int e^{t} cot (e^{t} - 8) d t

ln sin (e^{t} - 8) + C

Solution steps

\int e^{t} cot (e^{t} - 8) d t

Apply u-substitution

: \int cot (u) d u

= \int cot (u) d u

Rewrite using trig identities

= \int \frac{cos ( u )}{sin ( u )} d u

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= ln ∣ v ∣

Substitute back

= ln sin (e^{t} - 8)

Add a constant to the solution

= ln sin (e^{t} - 8) + C

\int \frac{x ^{3}}{( x ^{4} + 9 ) ^{4}} d x

\int x (x^{2} + 2)^{7} d x

\int \frac{1}{2} x^{\frac{3}{2}} d x

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

\int \frac{1}{x + 1 ^{5}} d x

What is the integral of e^tcot(e^t-8) ?
The integral of e^tcot(e^t-8) is ln|sin(e^t-8)|+C