What is the integral of y^3e^{2x} ?

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

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integral of y^3e^{2x}

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

\frac{e ^{2 x} y ^{4}}{4} + C

Solution steps

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

Take the constant out:

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

= e^{2 x} \cdot \int y^{3} d y

Apply the Power Rule

: \frac{y ^{4}}{4}

= e^{2 x} \frac{y ^{4}}{4}

Multiply fractions:

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

= \frac{e ^{2 x} y ^{4}}{4}

Add a constant to the solution

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

\frac{x}{1 - ln ( x - 2 )}

\int e^{- 8 t} d t

\frac{d}{d x} (e^{- t} cos (π x))

y^{^{''}} - 4 y = 9 e^{t}

\int 4 sec (4 x) tan (4 x) sec^{4} (4 x) d x

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