What is the integral of e^{11x}(11) ?

The integral of e^{11x}(11) is e^{11x}+C

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integral of e^{11x}(11)

\int e^{11 x} (11) d x

e^{11 x} + C

Solution steps

\int e^{11 x} \cdot 11 d x

Take the constant out:

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

= 11 \cdot \int e^{11 x} d x

Apply u-substitution

= 11 \cdot \int e^{u} \frac{1}{11} d u

Take the constant out:

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

= 11 \cdot \frac{1}{11} \cdot \int e^{u} d u

Use the common integral:

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

= 11 \cdot \frac{1}{11} e^{u}

Substitute back

u = 11 x

= 11 \cdot \frac{1}{11} e^{11 x}

Simplify

11 \cdot \frac{1}{11} e^{11 x} : e^{11 x}

= e^{11 x}

Add a constant to the solution

= e^{11 x} + C