Solve \int c^{2 x} d x

Evaluate

\int c^{2 x} d x

Use the substitution d x = \frac{1}{2} d t to transform the integral

More Steps

\int c^{2 x} \times \frac{1}{2} d t

Simplify

\int \frac{c ^{2 x}}{2} d t

Use the substitution t = 2 x to transform the integral

\int \frac{c ^{t}}{2} d t

Rewrite the expression

\int \frac{1}{2} c^{t} d t

Use the property of integral \int k f (x) d x = k \int f (x) d x

\frac{1}{2} \times \int c^{t} d t

Use the property of integral \int a^{x} d x = \frac{a ^{x}}{ln a}

\frac{1}{2} \times \frac{c ^{t}}{ln ( c )}

Multiply the terms

\frac{c ^{t}}{2 ln ( c )}

Substitute back

\frac{c ^{2 x}}{2 ln ( c )}

Solution

\frac{c ^{2 x}}{2 ln ( c )} + C, C \in R

Evaluate the integral