What is the integral of 10e^{5y} ?

The integral of 10e^{5y} is 2e^{5y}+C

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integral of 10e^{5y}

\int 10 e^{5 y} d y

2 e^{5 y} + C

Solution steps

\int 10 e^{5 y} d y

Take the constant out:

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

= 10 \cdot \int e^{5 y} d y

Apply u-substitution

= 10 \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

= 10 \cdot \frac{1}{5} \cdot \int e^{u} d u

Use the common integral:

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

= 10 \cdot \frac{1}{5} e^{u}

Substitute back

u = 5 y

= 10 \cdot \frac{1}{5} e^{5 y}

Simplify

10 \cdot \frac{1}{5} e^{5 y} : 2 e^{5 y}

= 2 e^{5 y}

Add a constant to the solution

= 2 e^{5 y} + C