Integral of xsiny dx

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 |  x*sin(y) dx
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$$\int\limits_{0}^{1} x \sin{\left(y \right)}\, dx$$

Integral(x*sin(y), (x, 0, 1))

Detail solution

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

$\int x \sin{\left(y \right)}\, dx = \sin{\left(y \right)} \int x\, dx$
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: $\frac{x^{2} \sin{\left(y \right)}}{2}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                   2       
 |                   x *sin(y)
 | x*sin(y) dx = C + ---------
 |                       2    
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$${{x^2\,\sin y}\over{2}}$$

Simplify

The answer [src]

sin(y)
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  2

$${{\sin y}\over{2}}$$

sin(y)
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  2

$$\frac{\sin{\left(y \right)}}{2}$$

Упростить

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