What is the integral of sin(xy) ?

The integral of sin(xy) is -1/y cos(yx)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(xy)

\int sin (x y) d x

- \frac{1}{y} cos (y x) + C

Solution steps

\int sin (x y) d x

Apply u-substitution

: \int \frac{sin ( u )}{y} d u

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{y} \cdot \int sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= \frac{1}{y} (- cos (u))

Substitute back

u = y x

= \frac{1}{y} (- cos (y x))

Simplify

= - \frac{1}{y} cos (y x)

Add a constant to the solution

= - \frac{1}{y} cos (y x) + C

\int_{- 1}^{x} 1.5 x^{2} d x

f (x) = \frac{x ^{5} + 4 x}{x ^{3}}

y^{^{'}} = (1 - y) \cdot sin (x)

\int_{2}^{3} \frac{18}{3 - x} d x

\int \frac{3 x ^{2} + 2}{( x ^{2} - 2 x + 2 ) ^{2}} d x