What is the integral of (e^{2y}-2y^3) ?

The integral of (e^{2y}-2y^3) is 1/2 e^{2y}-(y^4)/2+C

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integral of (e^{2y}-2y^3)

\int (e^{2 y} - 2 y^{3}) d y

\frac{1}{2} e^{2 y} - \frac{y ^{4}}{2} + C

Solution steps

\int e^{2 y} - 2 y^{3} d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int e^{2 y} d y - \int 2 y^{3} d y

\int e^{2 y} d y = \frac{1}{2} e^{2 y}

\int 2 y^{3} d y = \frac{y ^{4}}{2}

= \frac{1}{2} e^{2 y} - \frac{y ^{4}}{2}

Add a constant to the solution

= \frac{1}{2} e^{2 y} - \frac{y ^{4}}{2} + C

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What is the integral of (e^{2y}-2y^3) ?
The integral of (e^{2y}-2y^3) is 1/2 e^{2y}-(y^4)/2+C