What is the integral of e^{19x}(19) ?

The integral of e^{19x}(19) is e^{19x}+C

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integral of e^{19x}(19)

\int e^{19 x} (19) d x

e^{19 x} + C

Solution steps

\int e^{19 x} \cdot 19 d x

Take the constant out:

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

= 19 \cdot \int e^{19 x} d x

Apply u-substitution

= 19 \cdot \int e^{u} \frac{1}{19} d u

Take the constant out:

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

= 19 \cdot \frac{1}{19} \cdot \int e^{u} d u

Use the common integral:

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

= 19 \cdot \frac{1}{19} e^{u}

Substitute back

u = 19 x

= 19 \cdot \frac{1}{19} e^{19 x}

Simplify

19 \cdot \frac{1}{19} e^{19 x} : e^{19 x}

= e^{19 x}

Add a constant to the solution

= e^{19 x} + C