What is the integral of 2x^2ycos(x) ?

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

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integral of 2x^2ycos(x)

\int 2 x^{2} y cos (x) d y

x^{2} y^{2} cos (x) + C

Solution steps

\int 2 x^{2} y cos (x) d y

Take the constant out:

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

= 2 cos (x) x^{2} \cdot \int y d y

Apply the Power Rule

= 2 cos (x) x^{2} \frac{y ^{2}}{2}

Simplify

2 cos (x) x^{2} \frac{y ^{2}}{2} : x^{2} y^{2} cos (x)

= x^{2} y^{2} cos (x)

Add a constant to the solution

= x^{2} y^{2} cos (x) + C

\int \frac{x e ^{2 x}}{2 x + 1} d x

\int e^{2^{x}} d x

\int x ln (d) x d x

\int sec^{2} (5 x - 1) d x

\int \frac{- 2 x ^{2}}{x ^{2} - 2 x - 48} d x

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