Integral of (5cscxcotx-4sec²x)dx dx

The solution

You have entered [src]

  1                                 
  /                                 
 |                                  
 |  /                       2   \   
 |  \5*csc(x)*cot(x) - 4*sec (x)/ dx
 |                                  
/                                   
0

$$\int\limits_{0}^{1} \left(\cot{\left(x \right)} 5 \csc{\left(x \right)} - 4 \sec^{2}{\left(x \right)}\right)\, dx$$

Integral((5*csc(x))*cot(x) - 4*sec(x)^2, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \cot{\left(x \right)} 5 \csc{\left(x \right)}\, dx = - 5 \int \left(- \cot{\left(x \right)} \csc{\left(x \right)}\right)\, dx$
  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: $- 5 \csc{\left(x \right)}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 4 \sec^{2}{\left(x \right)}\right)\, dx = - 4 \int \sec^{2}{\left(x \right)}\, dx$
  1. $\int \sec^{2}{\left(x \right)}\, dx = \tan{\left(x \right)}$
  So, the result is: $- 4 \tan{\left(x \right)}$
The result is: $- 4 \tan{\left(x \right)} - 5 \csc{\left(x \right)}$
Now simplify:

$- 4 \tan{\left(x \right)} - \frac{5}{\sin{\left(x \right)}}$
Add the constant of integration:

$- 4 \tan{\left(x \right)} - \frac{5}{\sin{\left(x \right)}}+ \mathrm{constant}$

The answer is:

$- 4 \tan{\left(x \right)} - \frac{5}{\sin{\left(x \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                          
 |                                                           
 | /                       2   \                             
 | \5*csc(x)*cot(x) - 4*sec (x)/ dx = C - 5*csc(x) - 4*tan(x)
 |                                                           
/

$$\int \left(\cot{\left(x \right)} 5 \csc{\left(x \right)} - 4 \sec^{2}{\left(x \right)}\right)\, dx = C - 4 \tan{\left(x \right)} - 5 \csc{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

Numerical answer [src]

6.89661838974298e+19

6.89661838974298e+19

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (5cscxcotx-4sec²x)dx dx

Limits of integration:

The graph:

Piecewise:

The solution