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Integral calculus Calculator

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1

Solved example of Integral calculus

$\int\left(x^3+3x^2\cdot x​\right)dx+\int\left(x^3+3x^{2−3​}\right)dx$
2

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

$\int x^3dx+\int3x​x^2dx+\int x^3dx+\int3x^{2−3​}dx$
3

Adding $\int x^3dx$ and $\int x^3dx$

$\int3x​x^2dx+\int3x^{2−3​}dx+2\int x^3dx$
4

Take the constant out of the integral

$3\int x​x^2dx+\int3x^{2−3​}dx+2\int x^3dx$
5

Take the constant out of the integral

$3x​\int x^2dx+\int3x^{2−3​}dx+2\int x^3dx$
6

Take the constant out of the integral

$3x​\int x^2dx+3\int x^{2−3​}dx+2\int x^3dx$
7

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

$\frac{x​3x^{3}}{3}+3\int x^{2−3​}dx+2\int x^3dx$
8

Simplifying the fraction by $3$

$x​x^{3}+3\int x^{2−3​}dx+2\int x^3dx$
9

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

$x​x^{3}+\frac{3x^{\left(2−3​+1\right)}}{2−3​+1}+2\int x^3dx$
10

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

$x​x^{3}+\frac{3x^{\left(2−3​+1\right)}}{2−3​+1}+\frac{2x^{4}}{4}$
11

Take $\frac{2}{4}$ out of the fraction

$x​x^{3}+\frac{3x^{\left(2−3​+1\right)}}{2−3​+1}+\frac{1}{2}x^{4}$
12

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

$x​x^{3}+\frac{3x^{\left(2−3​+1\right)}}{2−3​+1}+\frac{1}{2}x^{4}+C_0$

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