Mister Exam

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y(1+x^2)
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Similar expressions
y(1-x^2)

Integral of y(1+x^2) dy

The solution

You have entered [src]

 3*x             
  /              
 |               
 |    /     2\   
 |  y*\1 + x / dy
 |               
/                
3*x

$$\int\limits_{3 x}^{3 x} y \left(x^{2} + 1\right)\, dy$$

Integral(y*(1 + x^2), (y, 3*x, 3*x))

Detail solution

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

$\int y \left(x^{2} + 1\right)\, dy = \left(x^{2} + 1\right) \int y\, dy$
1. The integral of $y^{n}$ is $\frac{y^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int y\, dy = \frac{y^{2}}{2}$
So, the result is: $\frac{y^{2} \left(x^{2} + 1\right)}{2}$
Add the constant of integration:

$\frac{y^{2} \left(x^{2} + 1\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{y^{2} \left(x^{2} + 1\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                      2 /     2\
 |   /     2\          y *\1 + x /
 | y*\1 + x / dy = C + -----------
 |                          2     
/

$$\int y \left(x^{2} + 1\right)\, dy = C + \frac{y^{2} \left(x^{2} + 1\right)}{2}$$

Simplify

The answer [src]

$$0$$

Numerical answer [src]

0.0

0.0

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

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Integral of y(1+x^2) dy

Limits of integration:

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The solution