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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 2/x^4
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Integral of (1-x^2)/(1+x^2)
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Integral of 1/(1+4x^2)
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Integral of x*dx/(x^2+1)
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Identical expressions
- dx/(x*(one +(lnx^ two)))
- dx divide by (x multiply by (1 plus (lnx squared )))
- dx divide by (x multiply by (one plus (lnx to the power of two)))
- dx/(x*(1+(lnx2)))
- dx/x*1+lnx2
- dx/(x*(1+(lnx²)))
- dx/(x*(1+(lnx to the power of 2)))
- dx/(x(1+(lnx^2)))
- dx/(x(1+(lnx2)))
- dx/x1+lnx2
- dx/x1+lnx^2
- dx divide by (x*(1+(lnx^2)))
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Similar expressions
- dx/(x*(1-(lnx^2)))
Integral of dx/(x*(1+(lnx^2))) dx
The solution
You have entered
[src]
x e / | | 1 | --------------- dx | / 2 \ | x*\1 + log (x)/ | / 1
$$\int\limits_{1}^{e^{x}} \frac{1}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx$$
Integral(1/(x*(1 + log(x)^2)), (x, 1, exp(x)))
The answer (Indefinite)
[src]
/ | | 1 / 2 \ | --------------- dx = C + RootSum\4*z + 1, i -> i*log(2*i + log(x))/ | / 2 \ | x*\1 + log (x)/ | /
$$\int \frac{1}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx = C + \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \log{\left(x \right)} \right)} \right)\right)}$$
The answer
[src]
/ 2 \ / 2 / / x\\\ - RootSum\4*z + 1, i -> i*log(2*i)/ + RootSum\4*z + 1, i -> i*log\2*i + log\e ///
$$- \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i \right)} \right)\right)} + \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \log{\left(e^{x} \right)} \right)} \right)\right)}$$
=
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/ 2 \ / 2 / / x\\\ - RootSum\4*z + 1, i -> i*log(2*i)/ + RootSum\4*z + 1, i -> i*log\2*i + log\e ///
$$- \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i \right)} \right)\right)} + \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \log{\left(e^{x} \right)} \right)} \right)\right)}$$
-RootSum(4*_z^2 + 1, Lambda(_i, _i*log(2*_i))) + RootSum(4*_z^2 + 1, Lambda(_i, _i*log(2*_i + log(exp(x)))))
Use the examples entering the upper and lower limits of integration.