Sr Examen
Integral de 1/((x-4)sqrt(t^2-15)) dx
Solución
Ha introducido
[src]
1 / | | 1 | -------------------- dx | _________ | / 2 | (x - 4)*\/ t - 15 | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{t^{2} - 15} \left(x - 4\right)}\, dx$$
Integral(1/((x - 4)*sqrt(t^2 - 15)), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / __________ __________\ \ / || | / 2 / 2 | __________ | | ||log\- 4*\/ -15 + t + x*\/ -15 + t / / 2 | | 1 ||---------------------------------------- for \/ -15 + t != 0| | -------------------- dx = C + |< __________ | | _________ || / 2 | | / 2 || \/ -15 + t | | (x - 4)*\/ t - 15 || | | \\ zoo*x otherwise / /
$$\int \frac{1}{\sqrt{t^{2} - 15} \left(x - 4\right)}\, dx = C + \begin{cases} \frac{\log{\left(x \sqrt{t^{2} - 15} - 4 \sqrt{t^{2} - 15} \right)}}{\sqrt{t^{2} - 15}} & \text{for}\: \sqrt{t^{2} - 15} \neq 0 \\\tilde{\infty} x & \text{otherwise} \end{cases}$$
Respuesta
[src]
/ __________\ / __________\
| / 2 | | / 2 |
log\-3*\/ -15 + t / log\-4*\/ -15 + t /
--------------------- - ---------------------
__________ __________
/ 2 / 2
\/ -15 + t \/ -15 + t
$$- \frac{\log{\left(- 4 \sqrt{t^{2} - 15} \right)}}{\sqrt{t^{2} - 15}} + \frac{\log{\left(- 3 \sqrt{t^{2} - 15} \right)}}{\sqrt{t^{2} - 15}}$$
=
=
/ __________\ / __________\
| / 2 | | / 2 |
log\-3*\/ -15 + t / log\-4*\/ -15 + t /
--------------------- - ---------------------
__________ __________
/ 2 / 2
\/ -15 + t \/ -15 + t
$$- \frac{\log{\left(- 4 \sqrt{t^{2} - 15} \right)}}{\sqrt{t^{2} - 15}} + \frac{\log{\left(- 3 \sqrt{t^{2} - 15} \right)}}{\sqrt{t^{2} - 15}}$$
log(-3*sqrt(-15 + t^2))/sqrt(-15 + t^2) - log(-4*sqrt(-15 + t^2))/sqrt(-15 + t^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.