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Integral of d{x}:
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Integral of 1/(x²+1)²
Identical expressions
(five ^- one)+(3cosx)^- one
(5 to the power of minus 1) plus (3 co sinus of e of x) to the power of minus 1
(five to the power of minus one) plus (3 co sinus of e of x) to the power of minus one
(5-1)+(3cosx)-1
5-1+3cosx-1
5^-1+3cosx^-1
(5^-1)+(3cosx)^-1dx
Similar expressions
(5^+1)+(3cosx)^-1
(5^-1)+(3cosx)^+1
(5^-1)-(3cosx)^-1

Solving integrals/ (5^-1)+(3cosx)^-1

Integral of (5^-1)+(3cosx)^-1 dx

The solution

You have entered [src]

  1                  
  /                  
 |                   
 |  /1      1    \   
 |  |- + --------| dx
 |  \5   3*cos(x)/   
 |                   
/                    
0

$$\int\limits_{0}^{1} \left(\frac{1}{5} + \frac{1}{3 \cos{\left(x \right)}}\right)\, dx$$

Integral(1/5 + 1/(3*cos(x)), (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \frac{1}{5}\, dx = \frac{x}{5}$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $- \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{3} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{3}$
The result is: $\frac{x}{5} - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{3} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{3}$
Add the constant of integration:

$\frac{x}{5} - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{3} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{3}+ \mathrm{constant}$

The answer is:

$\frac{x}{5} - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{3} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                           /        /x\\      /       /x\\    
 |                         log|-1 + tan|-||   log|1 + tan|-||    
 | /1      1    \             \        \2//      \       \2//   x
 | |- + --------| dx = C - ---------------- + --------------- + -
 | \5   3*cos(x)/                 3                  3          5
 |                                                               
/

$$\int \left(\frac{1}{5} + \frac{1}{3 \cos{\left(x \right)}}\right)\, dx = C + \frac{x}{5} - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{3} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1   log(1 - sin(1))   log(1 + sin(1))
- - --------------- + ---------------
5          6                 6

$$\frac{\log{\left(\sin{\left(1 \right)} + 1 \right)}}{6} + \frac{1}{5} - \frac{\log{\left(1 - \sin{\left(1 \right)} \right)}}{6}$$

1   log(1 - sin(1))   log(1 + sin(1))
- - --------------- + ---------------
5          6                 6

$$\frac{\log{\left(\sin{\left(1 \right)} + 1 \right)}}{6} + \frac{1}{5} - \frac{\log{\left(1 - \sin{\left(1 \right)} \right)}}{6}$$

Упростить

Numerical answer [src]

0.608730390294506

0.608730390294506

The graph

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

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Identical expressions

Similar expressions

Integral of (5^-1)+(3cosx)^-1 dx

Limits of integration:

The graph:

Piecewise:

The solution