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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of 1/(1+4x^2)
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Integral of (sec(x))^3
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Integral of x^2*e^(x^3)
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Integral of e^x²
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Identical expressions
- log one 0(x^ two +1)/x
- logarithm of 10(x squared plus 1) divide by x
- logarithm of one 0(x to the power of two plus 1) divide by x
- log10(x2+1)/x
- log10x2+1/x
- log10(x²+1)/x
- log10(x to the power of 2+1)/x
- log10x^2+1/x
- log10(x^2+1) divide by x
- log10(x^2+1)/xdx
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Similar expressions
- log10(x^2-1)/x
Integral of log10(x^2+1)/x dx
The solution
You have entered
[src]
3 / | | / / 2 \\ | |log\x + 1/| | |-----------| | \ log(10) / | ------------- dx | x | / 1
$$\int\limits_{1}^{3} \frac{\frac{1}{\log{\left(10 \right)}} \log{\left(x^{2} + 1 \right)}}{x}\, dx$$
Integral((log(x^2 + 1)/log(10))/x, (x, 1, 3))
The answer (Indefinite)
[src]
/ | | / / 2 \\ | |log\x + 1/| | |-----------| / 2 pi*I\ | \ log(10) / polylog\2, x *e / | ------------- dx = C - -------------------- | x 2*log(10) | /
$$\int \frac{\frac{1}{\log{\left(10 \right)}} \log{\left(x^{2} + 1 \right)}}{x}\, dx = C - \frac{\operatorname{Li}_{2}\left(x^{2} e^{i \pi}\right)}{2 \log{\left(10 \right)}}$$
The graph
The answer
[src]
/ pi*I\ 2
polylog\2, 9*e / pi
- ------------------- - ----------
2*log(10) 24*log(10)
$$- \frac{\pi^{2}}{24 \log{\left(10 \right)}} - \frac{\operatorname{Li}_{2}\left(9 e^{i \pi}\right)}{2 \log{\left(10 \right)}}$$
=
=
/ pi*I\ 2
polylog\2, 9*e / pi
- ------------------- - ----------
2*log(10) 24*log(10)
$$- \frac{\pi^{2}}{24 \log{\left(10 \right)}} - \frac{\operatorname{Li}_{2}\left(9 e^{i \pi}\right)}{2 \log{\left(10 \right)}}$$
-polylog(2, 9*exp_polar(pi*i))/(2*log(10)) - pi^2/(24*log(10))
Use the examples entering the upper and lower limits of integration.