Integral of e^(2x)

\int e^{2x}dx

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e
π
ln
log
lim
d/dx
d/dx
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sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
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sinh
cosh
tanh
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sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Answer

$\frac{1}{2}e^{2x}+C_0$

Step by step solution

Problem

$\int e^{2x}dx$
1

Solve the integral $\int e^{2x}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=2x \\ du=2dx\end{matrix}$
2

Isolate $dx$ in the previous equation

$\frac{du}{2}=dx$
3

Substituting $u$ and $dx$ in the integral

$\int\frac{e^u}{2}du$
4

Taking the constant out of the integral

$\frac{1}{2}\int e^udu$
5

The integral of the exponential function is given by the following formula $\displaystyle \int a^xdx=\frac{a^x}{\ln(a)}$, where $a > 0$ and $a \neq 1$

$\frac{1}{2}e^u$
6

Substitute $u$ back for it's value, $2x$

$\frac{1}{2}e^{2x}$
7

Add the constant of integration

$\frac{1}{2}e^{2x}+C_0$

Answer

$\frac{1}{2}e^{2x}+C_0$

Problem Analysis

Main topic:

Integration by trigonometric substitution

Time to solve it:

0.32 seconds

Views:

130