Integral of xx-3x

\int\left(x\cdot x-3x\right)dx

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asin
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Answer

$-\frac{3}{2}x^2+\frac{x^{3}}{3}+C_0$

Step by step solution

Problem

$\int\left(x\cdot x-3x\right)dx$
1

When multiplying exponents with same base you can add the exponents

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

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

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

Taking the constant out of the integral

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

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

$\frac{x^{3}}{3}-3\int xdx$
5

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

$\frac{x^{3}}{3}-3\cdot \frac{1}{2}x^2$
6

Multiply $\frac{1}{2}$ times $-3$

$\frac{x^{3}}{3}-\frac{3}{2}x^2$
7

Add the constant of integration

$-\frac{3}{2}x^2+\frac{x^{3}}{3}+C_0$

Answer

$-\frac{3}{2}x^2+\frac{x^{3}}{3}+C_0$

Problem Analysis

Main topic:

Integral calculus

Time to solve it:

0.25 seconds

Views:

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