Sr Examen
Integral de sqrt(4*x+6)/((2*x))-5 dx
Solución
Ha introducido
[src]
1 / | | / _________ \ | |\/ 4*x + 6 | | |----------- - 5| dx | \ 2*x / | / 0
$$\int\limits_{0}^{1} \left(-5 + \frac{\sqrt{4 x + 6}}{2 x}\right)\, dx$$
Integral(sqrt(4*x + 6)/((2*x)) - 5, (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ _________\ \
|| ___ |\/ 6 *\/ 4*x + 6 | |
/ ||-\/ 6 *acoth|-----------------| |
| || \ 6 / |
| / _________ \ ||-------------------------------- for 4*x + 6 > 6|
| |\/ 4*x + 6 | _________ || 6 |
| |----------- - 5| dx = C + \/ 4*x + 6 - 5*x + 6*|< |
| \ 2*x / || / ___ _________\ |
| || ___ |\/ 6 *\/ 4*x + 6 | |
/ ||-\/ 6 *atanh|-----------------| |
|| \ 6 / |
||-------------------------------- for 4*x + 6 < 6|
\\ 6 /
$$\int \left(-5 + \frac{\sqrt{4 x + 6}}{2 x}\right)\, dx = C - 5 x + \sqrt{4 x + 6} + 6 \left(\begin{cases} - \frac{\sqrt{6} \operatorname{acoth}{\left(\frac{\sqrt{6} \sqrt{4 x + 6}}{6} \right)}}{6} & \text{for}\: 4 x + 6 > 6 \\- \frac{\sqrt{6} \operatorname{atanh}{\left(\frac{\sqrt{6} \sqrt{4 x + 6}}{6} \right)}}{6} & \text{for}\: 4 x + 6 < 6 \end{cases}\right)$$
Gráfica
Respuesta
[src]
/ ____\
___ |\/ 15 |
oo - \/ 6 *acoth|------|
\ 3 /
$$- \sqrt{6} \operatorname{acoth}{\left(\frac{\sqrt{15}}{3} \right)} + \infty$$
=
=
/ ____\
___ |\/ 15 |
oo - \/ 6 *acoth|------|
\ 3 /
$$- \sqrt{6} \operatorname{acoth}{\left(\frac{\sqrt{15}}{3} \right)} + \infty$$
oo - sqrt(6)*acoth(sqrt(15)/3)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.