Sr Examen
Integral de (scrt(4+x))/(x+4scrt(x+4)) dx
Solución
Ha introducido
[src]
1 / | | _______ | \/ 4 + x | --------------- dx | _______ | x + 4*\/ x + 4 | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{x + 4}}{x + 4 \sqrt{x + 4}}\, dx$$
Integral(sqrt(4 + x)/(x + 4*sqrt(x + 4)), (x, 0, 1))
Respuesta (Indefinida)
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/ | | _______ / ___\ / ___\ | \/ 4 + x _______ | 3*\/ 2 | / _______ ___\ | 3*\/ 2 | / _______ ___\ | --------------- dx = C + 2*\/ 4 + x + 2*|-2 - -------|*log\2 + \/ 4 + x + 2*\/ 2 / + 2*|-2 + -------|*log\2 + \/ 4 + x - 2*\/ 2 / | _______ \ 2 / \ 2 / | x + 4*\/ x + 4 | /
$$\int \frac{\sqrt{x + 4}}{x + 4 \sqrt{x + 4}}\, dx = C + 2 \sqrt{x + 4} + 2 \left(- \frac{3 \sqrt{2}}{2} - 2\right) \log{\left(\sqrt{x + 4} + 2 + 2 \sqrt{2} \right)} + 2 \left(-2 + \frac{3 \sqrt{2}}{2}\right) \log{\left(\sqrt{x + 4} - 2 \sqrt{2} + 2 \right)}$$
Respuesta
[src]
1
/
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| / / / 2\ 2\
| | -3 | | / ___\ | / ___\ |
| |---------------------------------- for Or\And\x >= -4, x < -4 + 4*\1 - \/ 2 / /, x > -4 + 4*\1 - \/ 2 / /
/ ___\ ___ | | / 2\
-4 - 4*log\1 + 4*\/ 5 / + 2*\/ 5 + 4*log(8) + | < | / _______\ | dx
| | | \2 + \/ 4 + x / | _______
| |2*|1 - ----------------|*\/ 4 + x
| | \ 8 /
| \
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/
0
$$- 4 \log{\left(1 + 4 \sqrt{5} \right)} - 4 + \int\limits_{0}^{1} \begin{cases} - \frac{3}{2 \left(1 - \frac{\left(\sqrt{x + 4} + 2\right)^{2}}{8}\right) \sqrt{x + 4}} & \text{for}\: \left(x \geq -4 \wedge x < -4 + 4 \left(1 - \sqrt{2}\right)^{2}\right) \vee x > -4 + 4 \left(1 - \sqrt{2}\right)^{2} \end{cases}\, dx + 2 \sqrt{5} + 4 \log{\left(8 \right)}$$
=
=
1
/
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| / / / 2\ 2\
| | -3 | | / ___\ | / ___\ |
| |---------------------------------- for Or\And\x >= -4, x < -4 + 4*\1 - \/ 2 / /, x > -4 + 4*\1 - \/ 2 / /
/ ___\ ___ | | / 2\
-4 - 4*log\1 + 4*\/ 5 / + 2*\/ 5 + 4*log(8) + | < | / _______\ | dx
| | | \2 + \/ 4 + x / | _______
| |2*|1 - ----------------|*\/ 4 + x
| | \ 8 /
| \
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/
0
$$- 4 \log{\left(1 + 4 \sqrt{5} \right)} - 4 + \int\limits_{0}^{1} \begin{cases} - \frac{3}{2 \left(1 - \frac{\left(\sqrt{x + 4} + 2\right)^{2}}{8}\right) \sqrt{x + 4}} & \text{for}\: \left(x \geq -4 \wedge x < -4 + 4 \left(1 - \sqrt{2}\right)^{2}\right) \vee x > -4 + 4 \left(1 - \sqrt{2}\right)^{2} \end{cases}\, dx + 2 \sqrt{5} + 4 \log{\left(8 \right)}$$
-4 - 4*log(1 + 4*sqrt(5)) + 2*sqrt(5) + 4*log(8) + Integral(Piecewise((-3/(2*(1 - (2 + sqrt(4 + x))^2/8)*sqrt(4 + x)), (x > -4 + 4*(1 - sqrt(2))^2)∨((x >= -4)∧(x < -4 + 4*(1 - sqrt(2))^2)))), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.