Integral of -3x^2+1+x^3

\int\left(x^3-3x^2+1\right)dx

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Answer

$x-x^{3}+\frac{x^{4}}{4}+C_0$

Step by step solution

Problem

$\int\left(x^3-3x^2+1\right)dx$
1

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

$\int1dx+\int-3x^2dx+\int x^3dx$
2

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

$x+\int-3x^2dx+\int x^3dx$
3

Taking the constant out of the integral

$x-3\int x^2dx+\int x^3dx$
4

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

$x-3\frac{x^{3}}{3}+\int x^3dx$
5

Simplify the fraction

$x-x^{3}+\int x^3dx$
6

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

$x-x^{3}+\frac{x^{4}}{4}$
7

Add the constant of integration

$x-x^{3}+\frac{x^{4}}{4}+C_0$

Answer

$x-x^{3}+\frac{x^{4}}{4}+C_0$

Problem Analysis

Main topic:

Integral calculus

Time to solve it:

0.3 seconds

Views:

101