What is the integral of 3ye^{6y^2} ?

The integral of 3ye^{6y^2} is 1/4 e^{6y^2}+C

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integral of 3ye^{6y^2}

\int 3 y e^{6 y^{2}} d y

\frac{1}{4} e^{6 y^{2}} + C

Solution steps

\int 3 y e^{6 y^{2}} d y

Take the constant out:

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

= 3 \cdot \int y e^{6 y^{2}} d y

Apply u-substitution

: \int \frac{e ^{u}}{12} d u

= 3 \cdot \int \frac{e ^{u}}{12} d u

Take the constant out:

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

= 3 \cdot \frac{1}{12} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= 3 \cdot \frac{1}{12} e^{u}

Substitute back

u = 6 y^{2}

= 3 \cdot \frac{1}{12} e^{6 y^{2}}

Simplify

3 \cdot \frac{1}{12} e^{6 y^{2}} : \frac{1}{4} e^{6 y^{2}}

= \frac{1}{4} e^{6 y^{2}}

Add a constant to the solution

= \frac{1}{4} e^{6 y^{2}} + C

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What is the integral of 3ye^{6y^2} ?
The integral of 3ye^{6y^2} is 1/4 e^{6y^2}+C