Integral of cotgx dx

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 8/5             
  /              
 |               
 |  cot(a)*n*x dx
 |               
/                
0

$$\int\limits_{0}^{\frac{8}{5}} n x \cot{\left(a \right)}\, dx$$

Integral(cot(a)*n*x, (x, 0, 8/5))

Detail solution

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

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

$\frac{n x^{2} \cot{\left(a \right)}}{2}+ \mathrm{constant}$

The answer is:

$\frac{n x^{2} \cot{\left(a \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                       2       
 |                     n*x *cot(a)
 | cot(a)*n*x dx = C + -----------
 |                          2     
/

$${{\cot a\,n\,x^2}\over{2}}$$

Simplify

The answer [src]

32*n*cot(a)
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     25

$${{32\,\cot a\,n}\over{25}}$$

32*n*cot(a)
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     25

$$\frac{32 n \cot{\left(a \right)}}{25}$$

Упростить

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