What is the integral of 4ysin(xy) ?

The integral of 4ysin(xy) is -4cos(yx)+C

Popular >

integral of 4ysin(xy)

\int 4 y sin (x y) d x

- 4 cos (y x) + C

Solution steps

\int 4 y sin (x y) d x

Take the constant out:

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

= 4 y \cdot \int sin (y x) d x

Apply u-substitution

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

= 4 y \cdot \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

= 4 y \frac{1}{y} \cdot \int sin (u) d u

Use the common integral:

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

= 4 y \frac{1}{y} (- cos (u))

Substitute back

u = y x

= 4 y \frac{1}{y} (- cos (y x))

Simplify

4 y \frac{1}{y} (- cos (y x)) : - 4 cos (y x)

= - 4 cos (y x)

Add a constant to the solution

= - 4 cos (y x) + C

\frac{d}{d x} (A (- 2 e^{- 2 x} x + e^{- 2 x}))

\int_{0}^{1} 2 + 5 x^{2} d x

\frac{\partial}{\partial x} (x^{3} - 2 x y)

(2 x + 1)^{3} + \frac{2}{( 2 x + 1 ) ^{3}}

\frac{\partial}{\partial x} (4 + x + x^{2} Y (x))