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Identical expressions
(x-csc(x)cot(x))
(x minus csc(x) cotangent of (x))
x-cscxcotx
(x-csc(x)cot(x))dx
Similar expressions
(x+csc(x)cot(x))
(x-cosec(x)cot(x))
(x-cosecxcot(x))

Solving integrals/ (x-csc(x)cot(x))

Integral of (x-csc(x)cot(x)) dx

The solution

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  1                       
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 |  (x - csc(x)*cot(x)) dx
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0

$$\int\limits_{0}^{1} \left(- \cot{\left(x \right)} \csc{\left(x \right)} + x\right)\, dx$$

Simplify

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \cot{\left(x \right)} \csc{\left(x \right)}\right)\, dx = - \int \cot{\left(x \right)} \csc{\left(x \right)}\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \cot{\left(x \right)} \csc{\left(x \right)}\, dx = - \int \left(- \cot{\left(x \right)} \csc{\left(x \right)}\right)\, dx$
    1. The integral of cosecant times cotangent is cosecant:
      
      $\int \left(- \cot{\left(x \right)} \csc{\left(x \right)}\right)\, dx = \csc{\left(x \right)}$
    So, the result is: $- \csc{\left(x \right)}$
  So, the result is: $\csc{\left(x \right)}$
The result is: $\frac{x^{2}}{2} + \csc{\left(x \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

$${{1}\over{\sin x}}+{{x^2}\over{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-oo

$${\it \%a}$$

-oo

$$-\infty$$

Simplify

Numerical answer [src]

-1.3793236779486e+19

-1.3793236779486e+19

The graph

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

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Integral of (x-csc(x)cot(x)) dx

Limits of integration:

The graph:

Piecewise:

The solution