What is the integral of (cos(x)cos(y)-cot(x)) ?

The integral of (cos(x)cos(y)-cot(x)) is -ln|sin(x)|+cos(y)sin(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (cos(x)cos(y)-cot(x))

\int (cos (x) cos (y) - cot (x)) d x

- ln ∣ sin (x) ∣ + cos (y) sin (x) + C

Solution steps

\int cos (x) cos (y) - cot (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int cot (x) d x + \int cos (y) cos (x) d x

\int cot (x) d x = ln ∣ sin (x) ∣

\int cos (y) cos (x) d x = cos (y) sin (x)

= - ln ∣ sin (x) ∣ + cos (y) sin (x)

Add a constant to the solution

= - ln ∣ sin (x) ∣ + cos (y) sin (x) + C

\int e^{- t} cos (π t) d t

\int \frac{2 x + 7}{x ^{2} + 8 x + 16} d x

\int tan^{3} (y) d y

\int \frac{1}{( e ^{x} + 1 ) e ^{x}} d x

\int tan (x) csc (x) d x

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