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Integral Calculator

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1

Solved example of integral calculus

$\int 3x^2dx$
2

The integral of a constant by a function is equal to the constant multiplied by the integral of the function

$3\int x^2dx$

$3\left(\frac{x^{\left(2+1\right)}}{2+1}\right)$

Add the values $2$ and $1$

$3\left(\frac{x^{\left(2+1\right)}}{3}\right)$

Multiplying the fraction by $3$

$\frac{3x^{3}}{3}$

Take $\frac{3}{3}$ out of the fraction

$x^{3}$
3

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, such as $2$

$x^{3}$
4

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

$x^{3}+C_0$

Final Answer

$x^{3}+C_0$

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