Sr Examen
Integral de dx/(t^22+x-x^2) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------ dx | 22 2 | t + x - x | / 0
$$\int\limits_{0}^{1} \frac{1}{- x^{2} + \left(t^{22} + x\right)}\, dx$$
Integral(1/(t^22 + x - x^2), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ -1/2 + x \
atan|---------------|
| ___________|
/ | / 1 22 |
| | / - - - t |
| 1 \\/ 4 /
| ------------ dx = C - ---------------------
| 22 2 ___________
| t + x - x / 1 22
| / - - - t
/ \/ 4
$$\int \frac{1}{- x^{2} + \left(t^{22} + x\right)}\, dx = C - \frac{\operatorname{atan}{\left(\frac{x - \frac{1}{2}}{\sqrt{- t^{22} - \frac{1}{4}}} \right)}}{\sqrt{- t^{22} - \frac{1}{4}}}$$
Respuesta
[src]
/ ___________ \ / ___________ \ / ___________ \ / ___________ \
| / 1 | | / 1 | | / 1 | | / 1 |
| / --------- | | / --------- | | / --------- | | / --------- |
___________ | / 22 ___________| ___________ | / 22 ___________| ___________ | / 22 ___________| ___________ | / 22 ___________|
/ 1 |1 \/ 1 + 4*t 22 / 1 | / 1 | 1 \/ 1 + 4*t 22 / 1 | / 1 |1 \/ 1 + 4*t 22 / 1 | / 1 | 1 \/ 1 + 4*t 22 / 1 |
/ --------- *log|- + ---------------- + 2*t * / --------- | + / --------- *log|- - - ---------------- - 2*t * / --------- | - / --------- *log|- - ---------------- - 2*t * / --------- | - / --------- *log|- - + ---------------- + 2*t * / --------- |
/ 22 |2 2 / 22 | / 22 | 2 2 / 22 | / 22 |2 2 / 22 | / 22 | 2 2 / 22 |
\/ 1 + 4*t \ \/ 1 + 4*t / \/ 1 + 4*t \ \/ 1 + 4*t / \/ 1 + 4*t \ \/ 1 + 4*t / \/ 1 + 4*t \ \/ 1 + 4*t /
$$\sqrt{\frac{1}{4 t^{22} + 1}} \log{\left(- 2 t^{22} \sqrt{\frac{1}{4 t^{22} + 1}} - \frac{\sqrt{\frac{1}{4 t^{22} + 1}}}{2} - \frac{1}{2} \right)} - \sqrt{\frac{1}{4 t^{22} + 1}} \log{\left(- 2 t^{22} \sqrt{\frac{1}{4 t^{22} + 1}} - \frac{\sqrt{\frac{1}{4 t^{22} + 1}}}{2} + \frac{1}{2} \right)} - \sqrt{\frac{1}{4 t^{22} + 1}} \log{\left(2 t^{22} \sqrt{\frac{1}{4 t^{22} + 1}} + \frac{\sqrt{\frac{1}{4 t^{22} + 1}}}{2} - \frac{1}{2} \right)} + \sqrt{\frac{1}{4 t^{22} + 1}} \log{\left(2 t^{22} \sqrt{\frac{1}{4 t^{22} + 1}} + \frac{\sqrt{\frac{1}{4 t^{22} + 1}}}{2} + \frac{1}{2} \right)}$$
=
=
/ ___________ \ / ___________ \ / ___________ \ / ___________ \
| / 1 | | / 1 | | / 1 | | / 1 |
| / --------- | | / --------- | | / --------- | | / --------- |
___________ | / 22 ___________| ___________ | / 22 ___________| ___________ | / 22 ___________| ___________ | / 22 ___________|
/ 1 |1 \/ 1 + 4*t 22 / 1 | / 1 | 1 \/ 1 + 4*t 22 / 1 | / 1 |1 \/ 1 + 4*t 22 / 1 | / 1 | 1 \/ 1 + 4*t 22 / 1 |
/ --------- *log|- + ---------------- + 2*t * / --------- | + / --------- *log|- - - ---------------- - 2*t * / --------- | - / --------- *log|- - ---------------- - 2*t * / --------- | - / --------- *log|- - + ---------------- + 2*t * / --------- |
/ 22 |2 2 / 22 | / 22 | 2 2 / 22 | / 22 |2 2 / 22 | / 22 | 2 2 / 22 |
\/ 1 + 4*t \ \/ 1 + 4*t / \/ 1 + 4*t \ \/ 1 + 4*t / \/ 1 + 4*t \ \/ 1 + 4*t / \/ 1 + 4*t \ \/ 1 + 4*t /
$$\sqrt{\frac{1}{4 t^{22} + 1}} \log{\left(- 2 t^{22} \sqrt{\frac{1}{4 t^{22} + 1}} - \frac{\sqrt{\frac{1}{4 t^{22} + 1}}}{2} - \frac{1}{2} \right)} - \sqrt{\frac{1}{4 t^{22} + 1}} \log{\left(- 2 t^{22} \sqrt{\frac{1}{4 t^{22} + 1}} - \frac{\sqrt{\frac{1}{4 t^{22} + 1}}}{2} + \frac{1}{2} \right)} - \sqrt{\frac{1}{4 t^{22} + 1}} \log{\left(2 t^{22} \sqrt{\frac{1}{4 t^{22} + 1}} + \frac{\sqrt{\frac{1}{4 t^{22} + 1}}}{2} - \frac{1}{2} \right)} + \sqrt{\frac{1}{4 t^{22} + 1}} \log{\left(2 t^{22} \sqrt{\frac{1}{4 t^{22} + 1}} + \frac{\sqrt{\frac{1}{4 t^{22} + 1}}}{2} + \frac{1}{2} \right)}$$
sqrt(1/(1 + 4*t^22))*log(1/2 + sqrt(1/(1 + 4*t^22))/2 + 2*t^22*sqrt(1/(1 + 4*t^22))) + sqrt(1/(1 + 4*t^22))*log(-1/2 - sqrt(1/(1 + 4*t^22))/2 - 2*t^22*sqrt(1/(1 + 4*t^22))) - sqrt(1/(1 + 4*t^22))*log(1/2 - sqrt(1/(1 + 4*t^22))/2 - 2*t^22*sqrt(1/(1 + 4*t^22))) - sqrt(1/(1 + 4*t^22))*log(-1/2 + sqrt(1/(1 + 4*t^22))/2 + 2*t^22*sqrt(1/(1 + 4*t^22)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.