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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
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Integral of cot^5xdx
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Integral of (2x+1)^(1/2)
- Integral of 1/x*lnx
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Integral of -2e^(-2x)
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Identical expressions
- (sin(ax))/x
- ( sinus of (ax)) divide by x
- sinax/x
- (sin(ax)) divide by x
- (sin(ax))/xdx
Integral of (sin(ax))/x dx
The solution
You have entered
[src]
oo / | | sin(a*x) | -------- dx | x | / 0
$$\int\limits_{0}^{\infty} \frac{\sin{\left(a x \right)}}{x}\, dx$$
Integral(sin(a*x)/x, (x, 0, oo))
Detail solution
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Add the constant of integration:
SiRule(a=a, b=0, context=sin(a*x)/x, symbol=x)
The answer is:
The answer (Indefinite)
[src]
/ | | sin(a*x) | -------- dx = C + Si(a*x) | x | /
$$\int \frac{\sin{\left(a x \right)}}{x}\, dx = C + \operatorname{Si}{\left(a x \right)}$$
The answer
[src]
/ pi | -- for 2*|arg(a)| = 0 | 2 | | oo | / < | | | sin(a*x) | | -------- dx otherwise | | x | | |/ \0
$$\begin{cases} \frac{\pi}{2} & \text{for}\: 2 \left|{\arg{\left(a \right)}}\right| = 0 \\\int\limits_{0}^{\infty} \frac{\sin{\left(a x \right)}}{x}\, dx & \text{otherwise} \end{cases}$$
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/ pi | -- for 2*|arg(a)| = 0 | 2 | | oo | / < | | | sin(a*x) | | -------- dx otherwise | | x | | |/ \0
$$\begin{cases} \frac{\pi}{2} & \text{for}\: 2 \left|{\arg{\left(a \right)}}\right| = 0 \\\int\limits_{0}^{\infty} \frac{\sin{\left(a x \right)}}{x}\, dx & \text{otherwise} \end{cases}$$
Piecewise((pi/2, 2*Abs(arg(a)) = 0), (Integral(sin(a*x)/x, (x, 0, oo)), True))
Use the examples entering the upper and lower limits of integration.