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Identical expressions
- dz/(one +z+z^ seven)
- dz divide by (1 plus z plus z to the power of 7)
- dz divide by (one plus z plus z to the power of seven)
- dz/(1+z+z7)
- dz/1+z+z7
- dz/(1+z+z⁷)
- dz/1+z+z^7
- dz divide by (1+z+z^7)
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Similar expressions
- dz/(1-z+z^7)
- dz/(1+z-z^7)
Integral of dz/(1+z+z^7) dx
The solution
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[src]
1 / | | 1 | ---------- dz | 7 | 1 + z + z | / 0
$$\int\limits_{0}^{1} \frac{1}{z^{7} + \left(z + 1\right)}\, dz$$
Integral(1/(1 + z + z^7), (z, 0, 1))
The answer (Indefinite)
[src]
/ | / / 6 2 4 3 5\\ | 1 | 7 5 4 3 2 |46656 6766667424*t 2176567*t 10455222*t 23668632*t 113628348*t 1127777904*t || | ---------- dz = C + RootSum|870199*t - 27216*t - 15120*t - 3780*t - 504*t - 35*t - 1, t -> t*log|------ + z - ------------- + --------- + ----------- + ----------- + ------------ + -------------|| | 7 \ \117649 117649 117649 117649 117649 117649 117649 // | 1 + z + z | /
$$\int \frac{1}{z^{7} + \left(z + 1\right)}\, dz = C + \operatorname{RootSum} {\left(870199 t^{7} - 27216 t^{5} - 15120 t^{4} - 3780 t^{3} - 504 t^{2} - 35 t - 1, \left( t \mapsto t \log{\left(- \frac{6766667424 t^{6}}{117649} + \frac{1127777904 t^{5}}{117649} + \frac{23668632 t^{4}}{117649} + \frac{113628348 t^{3}}{117649} + \frac{10455222 t^{2}}{117649} + \frac{2176567 t}{117649} + z + \frac{46656}{117649} \right)} \right)\right)}$$
The answer
[src]
/ / 6 2 4 3 5\\ / / 6 2 4 3 5\\
| 7 5 4 3 2 |46656 6766667424*t 2176567*t 10455222*t 23668632*t 113628348*t 1127777904*t || | 7 5 4 3 2 |164305 6766667424*t 2176567*t 10455222*t 23668632*t 113628348*t 1127777904*t ||
- RootSum|870199*t - 27216*t - 15120*t - 3780*t - 504*t - 35*t - 1, t -> t*log|------ - ------------- + --------- + ----------- + ----------- + ------------ + -------------|| + RootSum|870199*t - 27216*t - 15120*t - 3780*t - 504*t - 35*t - 1, t -> t*log|------ - ------------- + --------- + ----------- + ----------- + ------------ + -------------||
\ \117649 117649 117649 117649 117649 117649 117649 // \ \117649 117649 117649 117649 117649 117649 117649 //
$$- \operatorname{RootSum} {\left(870199 t^{7} - 27216 t^{5} - 15120 t^{4} - 3780 t^{3} - 504 t^{2} - 35 t - 1, \left( t \mapsto t \log{\left(- \frac{6766667424 t^{6}}{117649} + \frac{1127777904 t^{5}}{117649} + \frac{23668632 t^{4}}{117649} + \frac{113628348 t^{3}}{117649} + \frac{10455222 t^{2}}{117649} + \frac{2176567 t}{117649} + \frac{46656}{117649} \right)} \right)\right)} + \operatorname{RootSum} {\left(870199 t^{7} - 27216 t^{5} - 15120 t^{4} - 3780 t^{3} - 504 t^{2} - 35 t - 1, \left( t \mapsto t \log{\left(- \frac{6766667424 t^{6}}{117649} + \frac{1127777904 t^{5}}{117649} + \frac{23668632 t^{4}}{117649} + \frac{113628348 t^{3}}{117649} + \frac{10455222 t^{2}}{117649} + \frac{2176567 t}{117649} + \frac{164305}{117649} \right)} \right)\right)}$$
=
=
/ / 6 2 4 3 5\\ / / 6 2 4 3 5\\
| 7 5 4 3 2 |46656 6766667424*t 2176567*t 10455222*t 23668632*t 113628348*t 1127777904*t || | 7 5 4 3 2 |164305 6766667424*t 2176567*t 10455222*t 23668632*t 113628348*t 1127777904*t ||
- RootSum|870199*t - 27216*t - 15120*t - 3780*t - 504*t - 35*t - 1, t -> t*log|------ - ------------- + --------- + ----------- + ----------- + ------------ + -------------|| + RootSum|870199*t - 27216*t - 15120*t - 3780*t - 504*t - 35*t - 1, t -> t*log|------ - ------------- + --------- + ----------- + ----------- + ------------ + -------------||
\ \117649 117649 117649 117649 117649 117649 117649 // \ \117649 117649 117649 117649 117649 117649 117649 //
$$- \operatorname{RootSum} {\left(870199 t^{7} - 27216 t^{5} - 15120 t^{4} - 3780 t^{3} - 504 t^{2} - 35 t - 1, \left( t \mapsto t \log{\left(- \frac{6766667424 t^{6}}{117649} + \frac{1127777904 t^{5}}{117649} + \frac{23668632 t^{4}}{117649} + \frac{113628348 t^{3}}{117649} + \frac{10455222 t^{2}}{117649} + \frac{2176567 t}{117649} + \frac{46656}{117649} \right)} \right)\right)} + \operatorname{RootSum} {\left(870199 t^{7} - 27216 t^{5} - 15120 t^{4} - 3780 t^{3} - 504 t^{2} - 35 t - 1, \left( t \mapsto t \log{\left(- \frac{6766667424 t^{6}}{117649} + \frac{1127777904 t^{5}}{117649} + \frac{23668632 t^{4}}{117649} + \frac{113628348 t^{3}}{117649} + \frac{10455222 t^{2}}{117649} + \frac{2176567 t}{117649} + \frac{164305}{117649} \right)} \right)\right)}$$
-RootSum(870199*_t^7 - 27216*_t^5 - 15120*_t^4 - 3780*_t^3 - 504*_t^2 - 35*_t - 1, Lambda(_t, _t*log(46656/117649 - 6766667424*_t^6/117649 + 2176567*_t/117649 + 10455222*_t^2/117649 + 23668632*_t^4/117649 + 113628348*_t^3/117649 + 1127777904*_t^5/117649))) + RootSum(870199*_t^7 - 27216*_t^5 - 15120*_t^4 - 3780*_t^3 - 504*_t^2 - 35*_t - 1, Lambda(_t, _t*log(164305/117649 - 6766667424*_t^6/117649 + 2176567*_t/117649 + 10455222*_t^2/117649 + 23668632*_t^4/117649 + 113628348*_t^3/117649 + 1127777904*_t^5/117649)))
Use the examples entering the upper and lower limits of integration.