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Identical expressions
xcos^2y
x co sinus of e of squared y
xcos2y
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xcos to the power of 2y
xcos^2ydx

Integral of xcos^2y dx

The solution

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  1             
  /             
 |              
 |       2      
 |  x*cos (y) dx
 |              
/               
0

$$\int\limits_{0}^{1} x \cos^{2}{\left(y \right)}\, dx$$

Integral(x*cos(y)^2, (x, 0, 1))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                             
 |                     2    2   
 |      2             x *cos (y)
 | x*cos (y) dx = C + ----------
 |                        2     
/

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

Simplify

The answer [src]

   2   
cos (y)
-------
   2

$$\frac{\cos^{2}{\left(y \right)}}{2}$$

   2   
cos (y)
-------
   2

$$\frac{\cos^{2}{\left(y \right)}}{2}$$

cos(y)^2/2

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

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Identical expressions

Integral of xcos^2y dx

Limits of integration:

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The solution