Mister Exam

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Integral of d{x}:
Integral of e^(x^2)
Integral of sin(x)^3
Integral of √(x^2+1)
Integral of cos(5x)
Identical expressions
two *x/y^ three
2 multiply by x divide by y cubed
two multiply by x divide by y to the power of three
2*x/y3
2*x/y³
2*x/y to the power of 3
2x/y^3
2x/y3
2*x divide by y^3
2*x/y^3dx

Solving integrals/ 2*x/y^3

Integral of 2*x/y^3 dx

The solution

You have entered [src]

$$\int\limits_{0}^{1} \frac{2 x}{y^{3}}\, dx$$

Integral((2*x)/y^3, (x, 0, 1))

Detail solution

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

$\int \frac{2 x}{y^{3}}\, dx = \frac{\int 2 x\, dx}{y^{3}}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2 x\, dx = 2 \int x\, dx$
  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: $x^{2}$
So, the result is: $\frac{x^{2}}{y^{3}}$
Add the constant of integration:

$\frac{x^{2}}{y^{3}}+ \mathrm{constant}$

The answer is:

$\frac{x^{2}}{y^{3}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /               
 |               2
 | 2*x          x 
 | --- dx = C + --
 |   3           3
 |  y           y 
 |                
/

$$\int \frac{2 x}{y^{3}}\, dx = C + \frac{x^{2}}{y^{3}}$$

Simplify

The answer [src]

1 
--
 3
y

$$\frac{1}{y^{3}}$$

=

1 
--
 3
y

$$\frac{1}{y^{3}}$$

y^(-3)

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