What is the integral of 5y^2(e^x)^2 ?

The integral of 5y^2(e^x)^2 is (5e^{2x}y^3)/3+C

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integral of 5y^2(e^x)^2

integral

5 y^{2} (e^{x})^{2}

\frac{5 e ^{2 x} y ^{3}}{3} + C

Solution steps

\int 5 y^{2} (e^{x})^{2} d y

Take the constant out:

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

= (e^{x})^{2} \cdot 5 \cdot \int y^{2} d y

(e^{x})^{2} = e^{2 x}

= 5 e^{2 x} \cdot \int y^{2} d y

Apply the Power Rule

= 5 e^{2 x} \frac{y ^{3}}{3}

Multiply fractions:

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

= \frac{5 e ^{2 x} y ^{3}}{3}

Add a constant to the solution

= \frac{5 e ^{2 x} y ^{3}}{3} + C

in t e g r a l sin^{3} (2 x)

in t e g r a l \frac{x}{( 2 x + 1 ) ^{2}}

in t e g r a l \frac{( 2 x - 3 )}{( x - 2 )}

in t e g r a l \frac{cos ( x )}{( 1 + sin ( x ) ) ^{3}}

in t e g r a l \frac{( x ^{4} + 3 )}{x}

What is the integral of 5y^2(e^x)^2 ?
The integral of 5y^2(e^x)^2 is (5e^{2x}y^3)/3+C