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- Improper integral
- Double Integral
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How to use it?
- Integral of d{x}:
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Integral of x^4/(1+x^2)
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Integral of x^5/(x^2+1)
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Integral of (tan(x))^2/(cos(x))^2
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Integral of sqrt(x^2+1)*dx/x
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Identical expressions
- sin(5x)sin(x/ two)
- sinus of (5x) sinus of (x divide by 2)
- sinus of (5x) sinus of (x divide by two)
- sin5xsinx/2
- sin(5x)sin(x divide by 2)
- sin(5x)sin(x/2)dx
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Similar expressions
- (sin(5x))*(sin(x/2))
Integral of sin(5x)sin(x/2) dx
The solution
You have entered
[src]
1 / | | /x\ | sin(5*x)*sin|-| dx | \2/ | / 0
$$\int\limits_{0}^{1} \sin{\left(5 x \right)} \sin{\left(\frac{x}{2} \right)}\, dx$$
Integral(sin(5*x)*sin(x/2), (x, 0, 1))
The graph
The answer
[src]
20*cos(5)*sin(1/2) 2*cos(1/2)*sin(5)
- ------------------ + -----------------
99 99
$$- \frac{20 \sin{\left(\frac{1}{2} \right)} \cos{\left(5 \right)}}{99} + \frac{2 \sin{\left(5 \right)} \cos{\left(\frac{1}{2} \right)}}{99}$$
=
=
20*cos(5)*sin(1/2) 2*cos(1/2)*sin(5)
- ------------------ + -----------------
99 99
$$- \frac{20 \sin{\left(\frac{1}{2} \right)} \cos{\left(5 \right)}}{99} + \frac{2 \sin{\left(5 \right)} \cos{\left(\frac{1}{2} \right)}}{99}$$
-20*cos(5)*sin(1/2)/99 + 2*cos(1/2)*sin(5)/99
Use the examples entering the upper and lower limits of integration.