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