Mister Exam
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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of (x^3+2)/(x^3-4x)
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Integral of x/(1-x^4)^(1/2)
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Integral of e^(4x)
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Integral of e^x/(e^x+2)
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Identical expressions
- ln(one /(five - three *cos(x)))
- ln(1 divide by (5 minus 3 multiply by co sinus of e of (x)))
- ln(one divide by (five minus three multiply by co sinus of e of (x)))
- ln(1/(5-3cos(x)))
- ln1/5-3cosx
- ln(1 divide by (5-3*cos(x)))
- ln(1/(5-3*cos(x)))dx
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Similar expressions
- ln(1/(5+3*cos(x)))
- ln(1/(5-3*cosx))
Integral of ln(1/(5-3*cos(x))) dx
The solution
You have entered
[src]
2*pi / | | / 1 \ | log|------------| dx | \5 - 3*cos(x)/ | / 0
$$\int\limits_{0}^{2 \pi} \log{\left(\frac{1}{5 - 3 \cos{\left(x \right)}} \right)}\, dx$$
Integral(log(1/(5 - 3*cos(x))), (x, 0, 2*pi))
The answer (Indefinite)
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/ / | | | / 1 \ | x*sin(x) / 1 \ | log|------------| dx = C - 3* | ------------- dx + x*log|------------| | \5 - 3*cos(x)/ | -5 + 3*cos(x) \5 - 3*cos(x)/ | | / /
$$\int \log{\left(\frac{1}{5 - 3 \cos{\left(x \right)}} \right)}\, dx = C + x \log{\left(\frac{1}{5 - 3 \cos{\left(x \right)}} \right)} - 3 \int \frac{x \sin{\left(x \right)}}{3 \cos{\left(x \right)} - 5}\, dx$$
The answer
[src]
2*pi / | | / 1 \ | log|------------| dx | \5 - 3*cos(x)/ | / 0
$$\int\limits_{0}^{2 \pi} \log{\left(\frac{1}{5 - 3 \cos{\left(x \right)}} \right)}\, dx$$
=
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2*pi / | | / 1 \ | log|------------| dx | \5 - 3*cos(x)/ | / 0
$$\int\limits_{0}^{2 \pi} \log{\left(\frac{1}{5 - 3 \cos{\left(x \right)}} \right)}\, dx$$
Integral(log(1/(5 - 3*cos(x))), (x, 0, 2*pi))
Use the examples entering the upper and lower limits of integration.