What is the integral of ysin(2x) ?

The integral of ysin(2x) is -1/2 ycos(2x)+C

Popular >

integral of ysin(2x)

\int y sin (2 x) d x

- \frac{1}{2} y cos (2 x) + C

Solution steps

\int y sin (2 x) d x

Take the constant out:

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

= y \cdot \int sin (2 x) d x

Apply u-substitution

: \int sin (u) \frac{1}{2} d u

= y \cdot \int sin (u) \frac{1}{2} d u

Take the constant out:

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

= y \frac{1}{2} \cdot \int sin (u) d u

Use the common integral:

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

= y \frac{1}{2} (- cos (u))

Substitute back

u = 2 x

= y \frac{1}{2} (- cos (2 x))

Simplify

= - \frac{1}{2} y cos (2 x)

Add a constant to the solution

= - \frac{1}{2} y cos (2 x) + C

\int (x^{2} + 1) sin (x^{3} + 3 x) d x

\int 6 x^{2} y - 3 x y d x

\int 4 x^{2} + 6 d x

\int 9 x - x^{3} d x

\int \frac{20 y ^{3}}{5 y ^{4} + 1} d y