Mister Exam

Other calculators


x*sec^2(x)

Integral of x*sec^2(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1             
  /             
 |              
 |       2      
 |  x*sec (x) dx
 |              
/               
0               
$$\int\limits_{0}^{1} x \sec^{2}{\left(x \right)}\, dx$$
Integral(x*sec(x)^2, (x, 0, 1))
Detail solution
  1. Use integration by parts:

    Let and let .

    Then .

    To find :

    Now evaluate the sub-integral.

  2. Rewrite the integrand:

  3. Let .

    Then let and substitute :

    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:

    Now substitute back in:

  4. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                         
 |                                          
 |      2                                   
 | x*sec (x) dx = C + x*tan(x) + log(cos(x))
 |                                          
/                                           
$${{\left(\sin ^2\left(2\,x\right)+\cos ^2\left(2\,x\right)+2\,\cos \left(2\,x\right)+1\right)\,\log \left(\sin ^2\left(2\,x\right)+ \cos ^2\left(2\,x\right)+2\,\cos \left(2\,x\right)+1\right)+4\,x\, \sin \left(2\,x\right)}\over{2\,\sin ^2\left(2\,x\right)+2\,\cos ^2 \left(2\,x\right)+4\,\cos \left(2\,x\right)+2}}$$
The graph
The answer [src]
log(cos(1)) + tan(1)
$${{\left(\sin ^22+\cos ^22+2\,\cos 2+1\right)\,\log \left(\sin ^22+ \cos ^22+2\,\cos 2+1\right)+4\,\sin 2}\over{2\,\sin ^22+2\,\cos ^22+ 4\,\cos 2+2}}-{{\log 4}\over{2}}$$
=
=
log(cos(1)) + tan(1)
$$\log{\left(\cos{\left(1 \right)} \right)} + \tan{\left(1 \right)}$$
Numerical answer [src]
0.941781254268888
0.941781254268888
The graph
Integral of x*sec^2(x) dx

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