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pi / | | sin(x)*cos(a*x) dx | / 0
$$\int\limits_{0}^{\pi} \sin{\left(x \right)} \cos{\left(a x \right)}\, dx$$
Integral(sin(x)*cos(a*x), (x, 0, pi))
The answer (Indefinite)
[src]
// 2 \
|| sin (x) |
/ || ------- for Or(a = -1, a = 1)|
| || 2 |
| sin(x)*cos(a*x) dx = C + |< |
| ||cos(x)*cos(a*x) a*sin(x)*sin(a*x) |
/ ||--------------- + ----------------- otherwise |
|| 2 2 |
\\ -1 + a -1 + a /
$$\int \sin{\left(x \right)} \cos{\left(a x \right)}\, dx = C + \begin{cases} \frac{\sin^{2}{\left(x \right)}}{2} & \text{for}\: a = -1 \vee a = 1 \\\frac{a \sin{\left(x \right)} \sin{\left(a x \right)}}{a^{2} - 1} + \frac{\cos{\left(x \right)} \cos{\left(a x \right)}}{a^{2} - 1} & \text{otherwise} \end{cases}$$
The answer
[src]
/ 0 for Or(a = -1, a = 1) | | 1 cos(pi*a) <- ------- - --------- otherwise | 2 2 | -1 + a -1 + a \
$$\begin{cases} 0 & \text{for}\: a = -1 \vee a = 1 \\- \frac{\cos{\left(\pi a \right)}}{a^{2} - 1} - \frac{1}{a^{2} - 1} & \text{otherwise} \end{cases}$$
=
=
/ 0 for Or(a = -1, a = 1) | | 1 cos(pi*a) <- ------- - --------- otherwise | 2 2 | -1 + a -1 + a \
$$\begin{cases} 0 & \text{for}\: a = -1 \vee a = 1 \\- \frac{\cos{\left(\pi a \right)}}{a^{2} - 1} - \frac{1}{a^{2} - 1} & \text{otherwise} \end{cases}$$
Piecewise((0, (a = -1)∨(a = 1)), (-1/(-1 + a^2) - cos(pi*a)/(-1 + a^2), True))
Use the examples entering the upper and lower limits of integration.