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Integrals of Exponential Functions Calculator

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1

Solved example of integrals of exponential functions

$\int\left(2x+7\right)e^{x^2+7x}dx$
2

Solve the integral $\int e^{\left(x^2+7x\right)}\left(2x+7\right)dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=e^{\left(x^2+7x\right)} \\ du=e^{\left(x^2+7x\right)}\left(2x+7\right)dx\end{matrix}$
3

Isolate $dx$ in the previous equation

$\frac{du}{e^{\left(x^2+7x\right)}\left(2x+7\right)}=dx$
4

Substituting $u$ and $dx$ in the integral and simplify

$\int1du$
5

The integral of a constant is equal to the constant times the integral's variable

$u$
6

Substitute $u$ back for it's value, $e^{\left(x^2+7x\right)}$

$e^{\left(x^2+7x\right)}$
7

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration

$e^{\left(x^2+7x\right)}+C_0$

Final Answer

$e^{\left(x^2+7x\right)}+C_0$

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