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Step-by-step Solution

Integral of $x^{10}+e^{5x}$

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Answer

$\frac{x^{11}}{11}+\frac{1}{5}e^{5x}+C_0$

Step-by-step explanation

Problem to solve:

$\int\left(x^{10}+e^{5x}\right)dx$
1

The integral of a sum of two or more functions is equal to the sum of their integrals

$\int x^{10}dx+\int e^{5x}dx$
2

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a constant function

$\frac{x^{11}}{11}+\int e^{5x}dx$

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Answer

$\frac{x^{11}}{11}+\frac{1}{5}e^{5x}+C_0$
$\int\left(x^{10}+e^{5x}\right)dx$

Main topic:

Integration by substitution

Used formulas:

5. See formulas

Time to solve it:

~ 0.72 seconds

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