Mister Exam

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Integral of d{x}:
Integral of sqrt(1+e^(2*x))
Integral of (x³+2x)
Integral of 1/3*t^3*dt
Integral of cos(x)*cos(kx)
Identical expressions
one / three *t^ three *dt
1 divide by 3 multiply by t cubed multiply by dt
one divide by three multiply by t to the power of three multiply by dt
1/3*t3*dt
1/3*t³*dt
1/3*t to the power of 3*dt
1/3t^3dt
1/3t3dt
1 divide by 3*t^3*dt

Solving integrals/ 1/3*t^3*dt

Integral of 1/3t^3dt dx

The solution

You have entered [src]

  0            
  /            
 |             
 |       3     
 |  1/3*t *1 dt
 |             
/              
0

$$\int\limits_{0}^{0} \frac{1}{3} t^{3} \cdot 1\, dt$$

Simplify

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{1}{3} t^{3} \cdot 1\, dt = \frac{\int t^{3}\, dt}{3}$
1. The integral of $t^{n}$ is $\frac{t^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int t^{3}\, dt = \frac{t^{4}}{4}$
So, the result is: $\frac{t^{4}}{12}$
Add the constant of integration:

$\frac{t^{4}}{12}+ \mathrm{constant}$

The answer is:

$\frac{t^{4}}{12}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                    
 |                    4
 |      3            t 
 | 1/3*t *1 dt = C + --
 |                   12
/

$${{t^4}\over{12}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$0$$

=

$$0$$

Simplify

Numerical answer [src]

0.0

0.0

The graph

Integral of 1/3*t^3*dt dx

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