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How to use it?
- Integral of d{x}:
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Integral of x^2/sqrt(1+x^2)
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Integral of x^5dx
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Integral of x^2/(x^3-1)
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Integral of x^2/sqrt(x^2-25)
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Identical expressions
- sin(x/ twelve)*sin(x/ three)
- sinus of (x divide by 12) multiply by sinus of (x divide by 3)
- sinus of (x divide by twelve) multiply by sinus of (x divide by three)
- sin(x/12)sin(x/3)
- sinx/12sinx/3
- sin(x divide by 12)*sin(x divide by 3)
- sin(x/12)*sin(x/3)dx
Integral of sin(x/12)*sin(x/3) dx
The solution
You have entered
[src]
1 / | | /x \ /x\ | sin|--|*sin|-| dx | \12/ \3/ | / 0
$$\int\limits_{0}^{1} \sin{\left(\frac{x}{12} \right)} \sin{\left(\frac{x}{3} \right)}\, dx$$
Integral(sin(x/12)*sin(x/3), (x, 0, 1))
The answer (Indefinite)
[src]
/ /5*x\ | 6*sin|---| | /x \ /x\ /x\ \ 12/ | sin|--|*sin|-| dx = C + 2*sin|-| - ---------- | \12/ \3/ \4/ 5 | /
$$\int \sin{\left(\frac{x}{12} \right)} \sin{\left(\frac{x}{3} \right)}\, dx = C + 2 \sin{\left(\frac{x}{4} \right)} - \frac{6 \sin{\left(\frac{5 x}{12} \right)}}{5}$$
The graph
The answer
[src]
16*cos(1/3)*sin(1/12) 4*cos(1/12)*sin(1/3)
- --------------------- + --------------------
5 5
$$- \frac{16 \sin{\left(\frac{1}{12} \right)} \cos{\left(\frac{1}{3} \right)}}{5} + \frac{4 \sin{\left(\frac{1}{3} \right)} \cos{\left(\frac{1}{12} \right)}}{5}$$
=
=
16*cos(1/3)*sin(1/12) 4*cos(1/12)*sin(1/3)
- --------------------- + --------------------
5 5
$$- \frac{16 \sin{\left(\frac{1}{12} \right)} \cos{\left(\frac{1}{3} \right)}}{5} + \frac{4 \sin{\left(\frac{1}{3} \right)} \cos{\left(\frac{1}{12} \right)}}{5}$$
-16*cos(1/3)*sin(1/12)/5 + 4*cos(1/12)*sin(1/3)/5
The graph
Use the examples entering the upper and lower limits of integration.