Mister Exam

Integral of 13xarctgxdx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                  
  /                  
 |                   
 |  13*x*atan(x)*1 dx
 |                   
/                    
0                    
$$\int\limits_{0}^{1} 13 x \operatorname{atan}{\left(x \right)} 1\, dx$$
Integral(13*x*atan(x)*1, (x, 0, 1))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    1. Use integration by parts:

      Let and let .

      Then .

      To find :

      1. The integral of is when :

      Now evaluate the sub-integral.

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

      1. Rewrite the integrand:

      2. Integrate term-by-term:

        1. The integral of a constant is the constant times the variable of integration:

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

          1. The integral of is .

          So, the result is:

        The result is:

      So, the result is:

    So, the result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                2        
 |                         13*x   13*atan(x)   13*x *atan(x)
 | 13*x*atan(x)*1 dx = C - ---- + ---------- + -------------
 |                          2         2              2      
/                                                           
$$\int 13 x \operatorname{atan}{\left(x \right)} 1\, dx = C + \frac{13 x^{2} \operatorname{atan}{\left(x \right)}}{2} - \frac{13 x}{2} + \frac{13 \operatorname{atan}{\left(x \right)}}{2}$$
The graph
The answer [src]
  13   13*pi
- -- + -----
  2      4  
$$- \frac{13}{2} + \frac{13 \pi}{4}$$
=
=
  13   13*pi
- -- + -----
  2      4  
$$- \frac{13}{2} + \frac{13 \pi}{4}$$
Numerical answer [src]
3.71017612416683
3.71017612416683
The graph
Integral of 13xarctgxdx dx

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