# Taylor series Calculator

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### Difficult Problems

1

Example

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

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

$\begin{matrix}u=2x \\ du=\frac{d}{dx}\left(u\right)dx\end{matrix}$
3

Isolate $dx$ in the previous equation

$\frac{du}{\frac{d}{dx}\left(u\right)}=dx$
4

Substituting $u$ and $dx$ in the integral

$\int\frac{e^u}{\frac{d}{dx}\left(u\right)}du$
5

The derivative of the linear function is equal to $1$

$\int e^udu$
6

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 $a \neq 1$

$e^u$
7

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

$e^{2x}$
8

$e^{2x}+C_0$