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How to use it?
- Integral of d{x}:
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Integral of x^3*e^(x^4)
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Integral of x^4*e^x
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Integral of (x^2+1)e^-x
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Integral of 1/(1+x^(1/2))
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Identical expressions
- ln(two *sin(x/ two)*xos(x))
- ln(2 multiply by sinus of (x divide by 2) multiply by xos(x))
- ln(two multiply by sinus of (x divide by two) multiply by xos(x))
- ln(2sin(x/2)xos(x))
- ln2sinx/2xosx
- ln(2*sin(x divide by 2)*xos(x))
- ln(2*sin(x/2)*xos(x))dx
Integral of ln(2*sin(x/2)*xos(x)) dx
The solution
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[src]
1 / | | / /x\ \ | log|2*sin|-|*x*cos(x)| dx | \ \2/ / | / 0
$$\int\limits_{0}^{1} \log{\left(x 2 \sin{\left(\frac{x}{2} \right)} \cos{\left(x \right)} \right)}\, dx$$
Integral(log(((2*sin(x/2))*x)*cos(x)), (x, 0, 1))
The answer (Indefinite)
[src]
/
|
| /x\
| x*cos|-|
| \2/
| -------- dx
| /x\
| sin|-|
/ | \2/ /
| | |
| / /x\ \ / / /x\ \ | x*sin(x)
| log|2*sin|-|*x*cos(x)| dx = C - x - -------------- + x*log|2*sin|-|*x*cos(x)| + | -------- dx
| \ \2/ / 2 \ \2/ / | cos(x)
| |
/ /
$$\int \log{\left(x 2 \sin{\left(\frac{x}{2} \right)} \cos{\left(x \right)} \right)}\, dx = C + x \log{\left(x 2 \sin{\left(\frac{x}{2} \right)} \cos{\left(x \right)} \right)} - x - \frac{\int \frac{x \cos{\left(\frac{x}{2} \right)}}{\sin{\left(\frac{x}{2} \right)}}\, dx}{2} + \int \frac{x \sin{\left(x \right)}}{\cos{\left(x \right)}}\, dx$$
Use the examples entering the upper and lower limits of integration.