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Solving integrals/ cos(a*x+b)

Integral of cos(a*x+b) dx

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
  1                
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 |  cos(a*x + b) dx
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0
$$\int\limits_{0}^{1} \cos{\left(a x + b \right)}\, dx$$ 
Integral(cos(a*x + b), (x, 0, 1))
The answer (Indefinite) [src] 
  /                      //sin(a*x + b)            \
 |                       ||------------  for a != 0|
 | cos(a*x + b) dx = C + |<     a                  |
 |                       ||                        |
/                        \\   sin(b)     otherwise /
$$\int \cos{\left(a x + b \right)}\, dx = C + \begin{cases} \frac{\sin{\left(a x + b \right)}}{a} & \text{for}\: a \neq 0 \\\sin{\left(b \right)} & \text{otherwise} \end{cases}$$
Simplify
The answer [src] 
/sin(a + b)   sin(b)                                  
|---------- - ------  for And(a > -oo, a < oo, a != 0)
<    a          a                                     
|                                                     
\      cos(b)                    otherwise
$$\begin{cases} - \frac{\sin{\left(b \right)}}{a} + \frac{\sin{\left(a + b \right)}}{a} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\\cos{\left(b \right)} & \text{otherwise} \end{cases}$$ 
=
= 
/sin(a + b)   sin(b)                                  
|---------- - ------  for And(a > -oo, a < oo, a != 0)
<    a          a                                     
|                                                     
\      cos(b)                    otherwise
$$\begin{cases} - \frac{\sin{\left(b \right)}}{a} + \frac{\sin{\left(a + b \right)}}{a} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\\cos{\left(b \right)} & \text{otherwise} \end{cases}$$ 
Piecewise((sin(a + b)/a - sin(b)/a, (a > -oo)∧(a < oo)∧(Ne(a, 0))), (cos(b), True))

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

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