Sr Examen
Integral de sqrt(a^2+x^2)/x dx
Solución
Ha introducido
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1 / | | _________ | / 2 2 | \/ a + x | ------------ dx | x | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{a^{2} + x^{2}}}{x}\, dx$$
Integral(sqrt(a^2 + x^2)/x, (x, 0, 1))
Respuesta (Indefinida)
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/
|
| _________
| / 2 2 2
| \/ a + x x /a\ a
| ------------ dx = C + -------------- - a*asinh|-| + ----------------
| x ________ \x/ ________
| / 2 / 2
/ / a / a
/ 1 + -- x* / 1 + --
/ 2 / 2
\/ x \/ x
$$\int \frac{\sqrt{a^{2} + x^{2}}}{x}\, dx = C + \frac{a^{2}}{x \sqrt{\frac{a^{2}}{x^{2}} + 1}} - a \operatorname{asinh}{\left(\frac{a}{x} \right)} + \frac{x}{\sqrt{\frac{a^{2}}{x^{2}} + 1}}$$
Respuesta
[src]
____
2 2 / 2
1 a a - a*\/ a *asinh(zoo*a)
----------- + ----------- - a*asinh(a) - ---------------------------
________ ________ ____
/ 2 / 2 / 2
\/ 1 + a \/ 1 + a \/ a
$$\frac{a^{2}}{\sqrt{a^{2} + 1}} - a \operatorname{asinh}{\left(a \right)} - \frac{a^{2} - a \sqrt{a^{2}} \operatorname{asinh}{\left(\tilde{\infty} a \right)}}{\sqrt{a^{2}}} + \frac{1}{\sqrt{a^{2} + 1}}$$
=
=
____
2 2 / 2
1 a a - a*\/ a *asinh(zoo*a)
----------- + ----------- - a*asinh(a) - ---------------------------
________ ________ ____
/ 2 / 2 / 2
\/ 1 + a \/ 1 + a \/ a
$$\frac{a^{2}}{\sqrt{a^{2} + 1}} - a \operatorname{asinh}{\left(a \right)} - \frac{a^{2} - a \sqrt{a^{2}} \operatorname{asinh}{\left(\tilde{\infty} a \right)}}{\sqrt{a^{2}}} + \frac{1}{\sqrt{a^{2} + 1}}$$
1/sqrt(1 + a^2) + a^2/sqrt(1 + a^2) - a*asinh(a) - (a^2 - a*sqrt(a^2)*asinh(±oo*a))/sqrt(a^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.