Integral of x^3+4x dx

The solution

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$$\int\limits_{0}^{1} \left(x^{3} + 4 x\right)\, dx$$

Integral(x^3 + 4*x, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{3}\, dx = \frac{x^{4}}{4}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 4 x\, dx = 4 \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $2 x^{2}$
The result is: $\frac{x^{4}}{4} + 2 x^{2}$
Now simplify:

$\frac{x^{2} \left(x^{2} + 8\right)}{4}$
Add the constant of integration:

$\frac{x^{2} \left(x^{2} + 8\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(x^{2} + 8\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

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$${{x^4}\over{4}}+2\,x^2$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

9/4

$${{9}\over{4}}$$

9/4

$$\frac{9}{4}$$

Simplify

Numerical answer [src]

2.25

2.25

The graph

Use the examples entering the upper and lower limits of integration.

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Integral of x^3+4x dx

Limits of integration:

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Piecewise:

The solution