Sr Examen
Integral de 1/(x^2+c)^3 dx
Solución
Ha introducido
[src]
1 / | | 1 | --------- dx | 3 | / 2 \ | \x + c/ | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(c + x^{2}\right)^{3}}\, dx$$
Integral(1/((x^2 + c)^3), (x, 0, 1))
Respuesta (Indefinida)
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_____ / _____\ _____ / _____\
/ -1 | 3 / -1 | / -1 | 3 / -1 |
/ 3* / --- *log|x - c * / --- | 3* / --- *log|x + c * / --- |
| 3 / 5 | / 5 | / 5 | / 5 |
| 1 3*x + 5*c*x \/ c \ \/ c / \/ c \ \/ c /
| --------- dx = C + ------------------------- - ----------------------------------- + -----------------------------------
| 3 4 2 4 3 2 16 16
| / 2 \ 8*c + 8*c *x + 16*c *x
| \x + c/
|
/
$$\int \frac{1}{\left(c + x^{2}\right)^{3}}\, dx = C - \frac{3 \sqrt{- \frac{1}{c^{5}}} \log{\left(- c^{3} \sqrt{- \frac{1}{c^{5}}} + x \right)}}{16} + \frac{3 \sqrt{- \frac{1}{c^{5}}} \log{\left(c^{3} \sqrt{- \frac{1}{c^{5}}} + x \right)}}{16} + \frac{5 c x + 3 x^{3}}{8 c^{4} + 16 c^{3} x^{2} + 8 c^{2} x^{4}}$$
Respuesta
[src]
_____ / _____\ _____ / _____\ _____ / _____\ _____ / _____\
/ -1 | 3 / -1 | / -1 | 3 / -1 | / -1 | 3 / -1 | / -1 | 3 / -1 |
3* / --- *log|c * / --- | 3* / --- *log|1 - c * / --- | 3* / --- *log|-c * / --- | 3* / --- *log|1 + c * / --- |
/ 5 | / 5 | / 5 | / 5 | / 5 | / 5 | / 5 | / 5 |
3 + 5*c \/ c \ \/ c / \/ c \ \/ c / \/ c \ \/ c / \/ c \ \/ c /
------------------- - ------------------------------- - ----------------------------------- + -------------------------------- + -----------------------------------
2 4 3 16 16 16 16
8*c + 8*c + 16*c
$$\frac{3 \sqrt{- \frac{1}{c^{5}}} \log{\left(- c^{3} \sqrt{- \frac{1}{c^{5}}} \right)}}{16} - \frac{3 \sqrt{- \frac{1}{c^{5}}} \log{\left(c^{3} \sqrt{- \frac{1}{c^{5}}} \right)}}{16} - \frac{3 \sqrt{- \frac{1}{c^{5}}} \log{\left(- c^{3} \sqrt{- \frac{1}{c^{5}}} + 1 \right)}}{16} + \frac{3 \sqrt{- \frac{1}{c^{5}}} \log{\left(c^{3} \sqrt{- \frac{1}{c^{5}}} + 1 \right)}}{16} + \frac{5 c + 3}{8 c^{4} + 16 c^{3} + 8 c^{2}}$$
=
=
_____ / _____\ _____ / _____\ _____ / _____\ _____ / _____\
/ -1 | 3 / -1 | / -1 | 3 / -1 | / -1 | 3 / -1 | / -1 | 3 / -1 |
3* / --- *log|c * / --- | 3* / --- *log|1 - c * / --- | 3* / --- *log|-c * / --- | 3* / --- *log|1 + c * / --- |
/ 5 | / 5 | / 5 | / 5 | / 5 | / 5 | / 5 | / 5 |
3 + 5*c \/ c \ \/ c / \/ c \ \/ c / \/ c \ \/ c / \/ c \ \/ c /
------------------- - ------------------------------- - ----------------------------------- + -------------------------------- + -----------------------------------
2 4 3 16 16 16 16
8*c + 8*c + 16*c
$$\frac{3 \sqrt{- \frac{1}{c^{5}}} \log{\left(- c^{3} \sqrt{- \frac{1}{c^{5}}} \right)}}{16} - \frac{3 \sqrt{- \frac{1}{c^{5}}} \log{\left(c^{3} \sqrt{- \frac{1}{c^{5}}} \right)}}{16} - \frac{3 \sqrt{- \frac{1}{c^{5}}} \log{\left(- c^{3} \sqrt{- \frac{1}{c^{5}}} + 1 \right)}}{16} + \frac{3 \sqrt{- \frac{1}{c^{5}}} \log{\left(c^{3} \sqrt{- \frac{1}{c^{5}}} + 1 \right)}}{16} + \frac{5 c + 3}{8 c^{4} + 16 c^{3} + 8 c^{2}}$$
(3 + 5*c)/(8*c^2 + 8*c^4 + 16*c^3) - 3*sqrt(-1/c^5)*log(c^3*sqrt(-1/c^5))/16 - 3*sqrt(-1/c^5)*log(1 - c^3*sqrt(-1/c^5))/16 + 3*sqrt(-1/c^5)*log(-c^3*sqrt(-1/c^5))/16 + 3*sqrt(-1/c^5)*log(1 + c^3*sqrt(-1/c^5))/16
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.