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- Integral of d{x}:
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Integral of e^(2*x)/x
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Integral of e^(2*x)/2
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Integral of (4-x^2)^0.5
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Integral of -2e^(-2x)
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Identical expressions
- sin(ax)cos(ax)
- sinus of (ax) co sinus of e of (ax)
- sinaxcosax
- sin(ax)cos(ax)dx
Integral of sin(ax)cos(ax) dx
The solution
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1 / | | sin(a*x)*cos(a*x) dx | / 0
$$\int\limits_{0}^{1} \sin{\left(a x \right)} \cos{\left(a x \right)}\, dx$$
Integral(sin(a*x)*cos(a*x), (x, 0, 1))
The answer (Indefinite)
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// 2 \
/ ||sin (a*x) |
| ||--------- for a != 0|
| sin(a*x)*cos(a*x) dx = C + |< 2*a |
| || |
/ || 0 otherwise |
\\ /
$$\int \sin{\left(a x \right)} \cos{\left(a x \right)}\, dx = C + \begin{cases} \frac{\sin^{2}{\left(a x \right)}}{2 a} & \text{for}\: a \neq 0 \\0 & \text{otherwise} \end{cases}$$
The answer
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/ 2 |sin (a) |------- for And(a > -oo, a < oo, a != 0) < 2*a | | 0 otherwise \
$$\begin{cases} \frac{\sin^{2}{\left(a \right)}}{2 a} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases}$$
=
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/ 2 |sin (a) |------- for And(a > -oo, a < oo, a != 0) < 2*a | | 0 otherwise \
$$\begin{cases} \frac{\sin^{2}{\left(a \right)}}{2 a} & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases}$$
Piecewise((sin(a)^2/(2*a), (a > -oo)∧(a < oo)∧(Ne(a, 0))), (0, True))
Use the examples entering the upper and lower limits of integration.