What is the integral of e^{nx} ?

The integral of e^{nx} is 1/n e^{nx}+C

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integral of e^{nx}

\int e^{n x} d x

\frac{1}{n} e^{n x} + C

Solution steps

\int e^{n x} d x

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{n} e^{u}

Substitute back

u = n x

= \frac{1}{n} e^{n x}

Add a constant to the solution

= \frac{1}{n} e^{n x} + C

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