What is the integral of 2ycos(y) ?

The integral of 2ycos(y) is 2(ysin(y)+cos(y))+C

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integral of 2ycos(y)

\int 2 y cos (y) d y

2 (y sin (y) + cos (y)) + C

Solution steps

\int 2 y cos (y) d y

Take the constant out:

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

= 2 \cdot \int y cos (y) d y

Apply Integration By Parts

: y sin (y) - \int sin (y) d y

= 2 (y sin (y) - \int sin (y) d y)

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

= 2 (y sin (y) - (- cos (y)))

Simplify

= 2 (y sin (y) + cos (y))

Add a constant to the solution

= 2 (y sin (y) + cos (y)) + C

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

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\int \frac{12 t ^{8} - t}{t ^{3}} d t

\int \frac{1}{( 1 - t ^{2} ) ^{\frac{3}{2}}} d t

What is the integral of 2ycos(y) ?
The integral of 2ycos(y) is 2(ysin(y)+cos(y))+C