Mister Exam

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How to use it?
Integral of d{x}:
Integral of x*sin(x)^2
Integral of x×sin^2
Integral of x^3/(4*x^2-8*x+5)
Integral of x(2-x)^2dx
Derivative of:
3x^6
Identical expressions
3x^ six
3x to the power of 6
3x to the power of six
3x6
3x⁶
3x^6dx

Solving integrals/ 3x^6

Integral of 3x^6 dx

The solution

You have entered [src]

$$\int\limits_{0}^{2} 3 x^{6}\, dx$$

Integral(3*x^6, (x, 0, 2))

Detail solution

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

$\int 3 x^{6}\, dx = 3 \int x^{6}\, dx$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{6}\, dx = \frac{x^{7}}{7}$
So, the result is: $\frac{3 x^{7}}{7}$
Add the constant of integration:

$\frac{3 x^{7}}{7}+ \mathrm{constant}$

The answer is:

$\frac{3 x^{7}}{7}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                  
 |                  7
 |    6          3*x 
 | 3*x  dx = C + ----
 |                7  
/

$$\int 3 x^{6}\, dx = C + \frac{3 x^{7}}{7}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

384/7

$$\frac{384}{7}$$

=

384/7

$$\frac{384}{7}$$

384/7

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