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- Improper integral
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How to use it?
- Integral of d{x}:
- Integral of 1/(1+x^5)
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Integral of (sinx)^2*(cosx)^2
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Integral of xe^-1
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Integral of x^3*ln(2x)
- Derivative of:
- 1/(1+x^5)
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Identical expressions
- one /(one +x^ five)
- 1 divide by (1 plus x to the power of 5)
- one divide by (one plus x to the power of five)
- 1/(1+x5)
- 1/1+x5
- 1/(1+x⁵)
- 1/1+x^5
- 1 divide by (1+x^5)
- 1/(1+x^5)dx
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Similar expressions
- 1/(1-x^5)
Integral of 1/(1+x^5) dx
The solution
You have entered
[src]
1 / | | 1 | ------ dx | 5 | 1 + x | / 0
$$\int\limits_{0}^{1} \frac{1}{x^{5} + 1}\, dx$$
Integral(1/(1 + x^5), (x, 0, 1))
The answer
[src]
/ 4 3 2 \ log(2) / 4 3 2 \
- RootSum\625*t + 125*t + 25*t + 5*t + 1, t -> t*log(5*t)/ + ------ + RootSum\625*t + 125*t + 25*t + 5*t + 1, t -> t*log(1 + 5*t)/
5
$$- \operatorname{RootSum} {\left(625 t^{4} + 125 t^{3} + 25 t^{2} + 5 t + 1, \left( t \mapsto t \log{\left(5 t \right)} \right)\right)} + \operatorname{RootSum} {\left(625 t^{4} + 125 t^{3} + 25 t^{2} + 5 t + 1, \left( t \mapsto t \log{\left(5 t + 1 \right)} \right)\right)} + \frac{\log{\left(2 \right)}}{5}$$
=
=
/ 4 3 2 \ log(2) / 4 3 2 \
- RootSum\625*t + 125*t + 25*t + 5*t + 1, t -> t*log(5*t)/ + ------ + RootSum\625*t + 125*t + 25*t + 5*t + 1, t -> t*log(1 + 5*t)/
5
$$- \operatorname{RootSum} {\left(625 t^{4} + 125 t^{3} + 25 t^{2} + 5 t + 1, \left( t \mapsto t \log{\left(5 t \right)} \right)\right)} + \operatorname{RootSum} {\left(625 t^{4} + 125 t^{3} + 25 t^{2} + 5 t + 1, \left( t \mapsto t \log{\left(5 t + 1 \right)} \right)\right)} + \frac{\log{\left(2 \right)}}{5}$$
-RootSum(625*_t^4 + 125*_t^3 + 25*_t^2 + 5*_t + 1, Lambda(_t, _t*log(5*_t))) + log(2)/5 + RootSum(625*_t^4 + 125*_t^3 + 25*_t^2 + 5*_t + 1, Lambda(_t, _t*log(1 + 5*_t)))
Use the examples entering the upper and lower limits of integration.