What is the integral of 7ye^{5x} ?

The integral of 7ye^{5x} is 7/5 ye^{5x}+C

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integral of 7ye^{5x}

\int 7 y e^{5 x} d x

\frac{7}{5} y e^{5 x} + C

Solution steps

\int 7 y e^{5 x} d x

Take the constant out:

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

= 7 y \cdot \int e^{5 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{5} d u

= 7 y \cdot \int e^{u} \frac{1}{5} d u

Take the constant out:

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

= 7 y \frac{1}{5} \cdot \int e^{u} d u

Use the common integral:

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

= 7 y \frac{1}{5} e^{u}

Substitute back

u = 5 x

= 7 y \frac{1}{5} e^{5 x}

Simplify

7 y \frac{1}{5} e^{5 x} : \frac{7}{5} y e^{5 x}

= \frac{7}{5} y e^{5 x}

Add a constant to the solution

= \frac{7}{5} y e^{5 x} + C

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