Mister Exam

Other calculators


(1+sinx)/(1+cosx)

Integral of (1+sinx)/(1+cosx) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1              
  /              
 |               
 |  1 + sin(x)   
 |  ---------- dx
 |  1 + cos(x)   
 |               
/                
0                
$$\int\limits_{0}^{1} \frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} + 1}\, dx$$
Integral((1 + sin(x))/(1 + cos(x)), (x, 0, 1))
Detail solution
  1. Rewrite the integrand:

  2. Integrate term-by-term:

    1. 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:

    1. Don't know the steps in finding this integral.

      But the integral is

    The result is:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                            
 |                                             
 | 1 + sin(x)                               /x\
 | ---------- dx = C - log(1 + cos(x)) + tan|-|
 | 1 + cos(x)                               \2/
 |                                             
/                                              
$$\int \frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} + 1}\, dx = C - \log{\left(\cos{\left(x \right)} + 1 \right)} + \tan{\left(\frac{x}{2} \right)}$$
The graph
The answer [src]
   /       2     \           
log\1 + tan (1/2)/ + tan(1/2)
$$\log{\left(\tan^{2}{\left(\frac{1}{2} \right)} + 1 \right)} + \tan{\left(\frac{1}{2} \right)}$$
=
=
   /       2     \           
log\1 + tan (1/2)/ + tan(1/2)
$$\log{\left(\tan^{2}{\left(\frac{1}{2} \right)} + 1 \right)} + \tan{\left(\frac{1}{2} \right)}$$
log(1 + tan(1/2)^2) + tan(1/2)
Numerical answer [src]
0.807470970731236
0.807470970731236
The graph
Integral of (1+sinx)/(1+cosx) dx

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