What is the integral of 13e^{13x-2} ?

The integral of 13e^{13x-2} is e^{13x-2}+C

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integral of 13e^{13x-2}

\int 13 e^{13 x - 2} d x

e^{13 x - 2} + C

Solution steps

\int 13 e^{13 x - 2} d x

Take the constant out:

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

= 13 \cdot \int e^{13 x - 2} d x

Apply u-substitution

: \int e^{u} \frac{1}{13} d u

= 13 \cdot \int e^{u} \frac{1}{13} d u

Take the constant out:

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

= 13 \cdot \frac{1}{13} \cdot \int e^{u} d u

Use the common integral:

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

= 13 \cdot \frac{1}{13} e^{u}

Substitute back

u = 13 x - 2

= 13 \cdot \frac{1}{13} e^{13 x - 2}

Simplify

13 \cdot \frac{1}{13} e^{13 x - 2} : e^{13 x - 2}

= e^{13 x - 2}

Add a constant to the solution

= e^{13 x - 2} + C

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What is the integral of 13e^{13x-2} ?
The integral of 13e^{13x-2} is e^{13x-2}+C