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Solving integrals/ sinaxdx

Integral of sinaxdx dx

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |  sin(a*x) dx
 |             
/              
0
∫01sin⁡(ax) dx\int\limits_{0}^{1} \sin{\left(a x \right)}\, dx 
Integral(sin(a*x), (x, 0, 1))
The answer (Indefinite) [src] 
  /                  //-cos(a*x)             \
 |                   ||----------  for a != 0|
 | sin(a*x) dx = C + |<    a                 |
 |                   ||                      |
/                    \\    0       otherwise /
∫sin⁡(ax) dx=C+{−cos⁡(ax)afor a≠00otherwise\int \sin{\left(a x \right)}\, dx = C + \begin{cases} - \frac{\cos{\left(a x \right)}}{a} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}
Simplify
The answer [src] 
/1   cos(a)                                  
|- - ------  for And(a > -oo, a < oo, a != 0)
{−cos⁡(a)a+1afor a>−∞∧a<∞∧a≠00otherwise\begin{cases} - \frac{\cos{\left(a \right)}}{a} + \frac{1}{a} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases} 
=
= 
/1   cos(a)                                  
|- - ------  for And(a > -oo, a < oo, a != 0)
{−cos⁡(a)a+1afor a>−∞∧a<∞∧a≠00otherwise\begin{cases} - \frac{\cos{\left(a \right)}}{a} + \frac{1}{a} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases} 
Piecewise((1/a - cos(a)/a, (a > -oo)∧(a < oo)∧(Ne(a, 0))), (0, True))

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