Sr Examen
Integral de dx/(sqrt9+x^2) dx
Solución
Ha introducido
[src]
1 / | | 1 | -------- dx | 29 2 | t + x | / 0
$$\int\limits_{0}^{1} \frac{1}{t^{29} + x^{2}}\, dx$$
Integral(1/(t^29 + x^2), (x, 0, 1))
Solución detallada
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Integral es .
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Añadimos la constante de integración:
Respuesta:
Respuesta (Indefinida)
[src]
/ x \
atan|--------|
/ | _____|
| | / 29 |
| 1 \\/ t /
| -------- dx = C + --------------
| 29 2 _____
| t + x / 29
| \/ t
/
$$\int \frac{1}{t^{29} + x^{2}}\, dx = C + \frac{\operatorname{atan}{\left(\frac{x}{\sqrt{t^{29}}} \right)}}{\sqrt{t^{29}}}$$
Respuesta
[src]
_____ / _____\ _____ / _____\ _____ / _____\ _____ / _____\
/ -1 | 29 / -1 | / -1 | 29 / -1 | / -1 | 29 / -1 | / -1 | 29 / -1 |
/ --- *log|-t * / --- | / --- *log|1 + t * / --- | / --- *log|t * / --- | / --- *log|1 - t * / --- |
/ 29 | / 29 | / 29 | / 29 | / 29 | / 29 | / 29 | / 29 |
\/ t \ \/ t / \/ t \ \/ t / \/ t \ \/ t / \/ t \ \/ t /
------------------------------- + ---------------------------------- - ------------------------------ - ----------------------------------
2 2 2 2
$$\frac{\sqrt{- \frac{1}{t^{29}}} \log{\left(- t^{29} \sqrt{- \frac{1}{t^{29}}} \right)}}{2} - \frac{\sqrt{- \frac{1}{t^{29}}} \log{\left(t^{29} \sqrt{- \frac{1}{t^{29}}} \right)}}{2} - \frac{\sqrt{- \frac{1}{t^{29}}} \log{\left(- t^{29} \sqrt{- \frac{1}{t^{29}}} + 1 \right)}}{2} + \frac{\sqrt{- \frac{1}{t^{29}}} \log{\left(t^{29} \sqrt{- \frac{1}{t^{29}}} + 1 \right)}}{2}$$
=
=
_____ / _____\ _____ / _____\ _____ / _____\ _____ / _____\
/ -1 | 29 / -1 | / -1 | 29 / -1 | / -1 | 29 / -1 | / -1 | 29 / -1 |
/ --- *log|-t * / --- | / --- *log|1 + t * / --- | / --- *log|t * / --- | / --- *log|1 - t * / --- |
/ 29 | / 29 | / 29 | / 29 | / 29 | / 29 | / 29 | / 29 |
\/ t \ \/ t / \/ t \ \/ t / \/ t \ \/ t / \/ t \ \/ t /
------------------------------- + ---------------------------------- - ------------------------------ - ----------------------------------
2 2 2 2
$$\frac{\sqrt{- \frac{1}{t^{29}}} \log{\left(- t^{29} \sqrt{- \frac{1}{t^{29}}} \right)}}{2} - \frac{\sqrt{- \frac{1}{t^{29}}} \log{\left(t^{29} \sqrt{- \frac{1}{t^{29}}} \right)}}{2} - \frac{\sqrt{- \frac{1}{t^{29}}} \log{\left(- t^{29} \sqrt{- \frac{1}{t^{29}}} + 1 \right)}}{2} + \frac{\sqrt{- \frac{1}{t^{29}}} \log{\left(t^{29} \sqrt{- \frac{1}{t^{29}}} + 1 \right)}}{2}$$
sqrt(-1/t^29)*log(-t^29*sqrt(-1/t^29))/2 + sqrt(-1/t^29)*log(1 + t^29*sqrt(-1/t^29))/2 - sqrt(-1/t^29)*log(t^29*sqrt(-1/t^29))/2 - sqrt(-1/t^29)*log(1 - t^29*sqrt(-1/t^29))/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.