Sr Examen
Integral de sqrt((a^2+x^2)+1) dx
Solución
Ha introducido
[src]
1 / | | _____________ | / 2 2 | \/ a + x + 1 dx | / 0
$$\int\limits_{0}^{1} \sqrt{\left(a^{2} + x^{2}\right) + 1}\, dx$$
Integral(sqrt(a^2 + x^2 + 1), (x, 0, 1))
Respuesta (Indefinida)
[src]
________________________ ________________________
/ 2 / 2
/ x / 2\ / x \ 2 / x / 2\ / x \
/ / 1 + ------------------ *\1 + a /*asinh|-----------------------| a * / 1 + ------------------ *\1 + a /*asinh|-----------------------|
| ____________________ ____________________ ____________________ / / 2\ | ____________________| / / 2\ | ____________________|
| _____________ / / 2\ 3 / / 2\ 2 / / 2\ \/ polar_lift\1 + a / | / / 2\ | \/ polar_lift\1 + a / | / / 2\ |
| / 2 2 x*\/ polar_lift\1 + a / x *\/ polar_lift\1 + a / x*a *\/ polar_lift\1 + a / \\/ polar_lift\1 + a / / \\/ polar_lift\1 + a / /
| \/ a + x + 1 dx = C + ---------------------------------------------------------------------- + ---------------------------------------------------------------------- + ---------------------------------------------------------------------- + ---------------------------------------------------------------------- + -------------------------------------------------------------------------
| ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
/ / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2
/ x 2 / x / x 2 / x / x 2 / x / x 2 / x / x 2 / x
2* / 1 + ------------------ + 2*a * / 1 + ------------------ 2* / 1 + ------------------ + 2*a * / 1 + ------------------ 2* / 1 + ------------------ + 2*a * / 1 + ------------------ 2* / 1 + ------------------ + 2*a * / 1 + ------------------ 2* / 1 + ------------------ + 2*a * / 1 + ------------------
/ / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\ / / 2\
\/ polar_lift\1 + a / \/ polar_lift\1 + a / \/ polar_lift\1 + a / \/ polar_lift\1 + a / \/ polar_lift\1 + a / \/ polar_lift\1 + a / \/ polar_lift\1 + a / \/ polar_lift\1 + a / \/ polar_lift\1 + a / \/ polar_lift\1 + a /
$$\int \sqrt{\left(a^{2} + x^{2}\right) + 1}\, dx = C + \frac{a^{2} x \sqrt{\operatorname{polar\_lift}{\left(a^{2} + 1 \right)}}}{2 a^{2} \sqrt{\frac{x^{2}}{\operatorname{polar\_lift}{\left(a^{2} + 1 \right)}} + 1} + 2 \sqrt{\frac{x^{2}}{\operatorname{polar\_lift}{\left(a^{2} + 1 \right)}} + 1}} + \frac{a^{2} \left(a^{2} + 1\right) \sqrt{\frac{x^{2}}{\operatorname{polar\_lift}{\left(a^{2} + 1 \right)}} + 1} \operatorname{asinh}{\left(\frac{x}{\sqrt{\operatorname{polar\_lift}{\left(a^{2} + 1 \right)}}} \right)}}{2 a^{2} \sqrt{\frac{x^{2}}{\operatorname{polar\_lift}{\left(a^{2} + 1 \right)}} + 1} + 2 \sqrt{\frac{x^{2}}{\operatorname{polar\_lift}{\left(a^{2} + 1 \right)}} + 1}} + \frac{x^{3} \sqrt{\operatorname{polar\_lift}{\left(a^{2} + 1 \right)}}}{2 a^{2} \sqrt{\frac{x^{2}}{\operatorname{polar\_lift}{\left(a^{2} + 1 \right)}} + 1} + 2 \sqrt{\frac{x^{2}}{\operatorname{polar\_lift}{\left(a^{2} + 1 \right)}} + 1}} + \frac{x \sqrt{\operatorname{polar\_lift}{\left(a^{2} + 1 \right)}}}{2 a^{2} \sqrt{\frac{x^{2}}{\operatorname{polar\_lift}{\left(a^{2} + 1 \right)}} + 1} + 2 \sqrt{\frac{x^{2}}{\operatorname{polar\_lift}{\left(a^{2} + 1 \right)}} + 1}} + \frac{\left(a^{2} + 1\right) \sqrt{\frac{x^{2}}{\operatorname{polar\_lift}{\left(a^{2} + 1 \right)}} + 1} \operatorname{asinh}{\left(\frac{x}{\sqrt{\operatorname{polar\_lift}{\left(a^{2} + 1 \right)}}} \right)}}{2 a^{2} \sqrt{\frac{x^{2}}{\operatorname{polar\_lift}{\left(a^{2} + 1 \right)}} + 1} + 2 \sqrt{\frac{x^{2}}{\operatorname{polar\_lift}{\left(a^{2} + 1 \right)}} + 1}}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.