What is the integral of y^2e^{sin(2x)} ?

The integral of y^2e^{sin(2x)} is (e^{sin(2x)}y^3)/3+C

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integral of y^2e^{sin(2x)}

\int y^{2} e^{s i n (2 x)}

\frac{e ^{s i n (2 x)} y ^{3}}{3} + C

Solution steps

\int y^{2} e^{s i n (2 x)} d y

Take the constant out:

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

= e^{s i n (2 x)} \cdot \int y^{2} d y

Apply the Power Rule

= e^{s i n (2 x)} \frac{y ^{3}}{3}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{e ^{s i n (2 x)} y ^{3}}{3}

Add a constant to the solution

= \frac{e ^{s i n (2 x)} y ^{3}}{3} + C

What is the integral of y^2e^{sin(2x)} ?
The integral of y^2e^{sin(2x)} is (e^{sin(2x)}y^3)/3+C