Integrate e^(4x)

\int e^{4x}dx

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Answer

$\frac{1}{4}e^{4x}+C_0$

Step by step solution

Problem

$\int e^{4x}dx$
1

Solve the integral $\int e^{4x}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=4x \\ du=4dx\end{matrix}$
2

Isolate $dx$ in the previous equation

$\frac{du}{4}=dx$
3

Substituting $u$ and $dx$ in the integral

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

Taking the constant out of the integral

$\frac{1}{4}\int e^udu$
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 $a \neq 1$

$\frac{1}{4}e^u$
6

Substitute $u$ back for it's value, $4x$

$\frac{1}{4}e^{4x}$
7

Add the constant of integration

$\frac{1}{4}e^{4x}+C_0$

Answer

$\frac{1}{4}e^{4x}+C_0$

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Problem Analysis

Main topic:

Integration by substitution

Time to solve it:

0.21 seconds

Views:

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