Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of dx/tan5x
Integral of (3-sin(x))/(2cos(x)+3tan(x))
Integral of 1/(x^4+4x^2+4)
Integral of 1/(sqrt(x))
Identical expressions
(x^ three +4x)/x
(x cubed plus 4x) divide by x
(x to the power of three plus 4x) divide by x
(x3+4x)/x
x3+4x/x
(x³+4x)/x
(x to the power of 3+4x)/x
x^3+4x/x
(x^3+4x) divide by x
(x^3+4x)/xdx
Similar expressions
(x^3-4x)/x

Solving integrals/ (x^3+4x)/x

Integral of (x^3+4x)/x dx

The solution

You have entered [src]

  1            
  /            
 |             
 |   3         
 |  x  + 4*x   
 |  -------- dx
 |     x       
 |             
/              
0

$$\int\limits_{0}^{1} \frac{x^{3} + 4 x}{x}\, dx$$

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

Detail solution

Rewrite the integrand:

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

$\frac{x \left(x^{2} + 12\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} + 12\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} + 12\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                          
 |                           
 |  3                       3
 | x  + 4*x                x 
 | -------- dx = C + 4*x + --
 |    x                    3 
 |                           
/

$${{x^3+12\,x}\over{3}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

13/3

$${{13}\over{3}}$$

13/3

$$\frac{13}{3}$$

Simplify

Numerical answer [src]

4.33333333333333

4.33333333333333

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (x^3+4x)/x dx

Limits of integration:

The graph:

Piecewise:

The solution