Sr Examen
Integral de (dx)/(3+sqrt(x)/(x+1)) dx
Solución
Ha introducido
[src]
24 / | | 1 | --------- dx | ___ | \/ x | 3 + ----- | x + 1 | / 15
$$\int\limits_{15}^{24} \frac{1}{\frac{\sqrt{x}}{x + 1} + 3}\, dx$$
Integral(1/(3 + sqrt(x)/(x + 1)), (x, 15, 24))
Respuesta (Indefinida)
[src]
/ ____ /1 ___\\
|6*\/ 35 *|- + \/ x ||
/ ____ | \6 /|
| ___ / ___ \ 34*\/ 35 *atan|--------------------|
| 1 2*\/ x x log\3 + \/ x + 3*x/ \ 35 /
| --------- dx = C - ------- + - + -------------------- + ------------------------------------
| ___ 9 3 27 945
| \/ x
| 3 + -----
| x + 1
|
/
$$\int \frac{1}{\frac{\sqrt{x}}{x + 1} + 3}\, dx = C - \frac{2 \sqrt{x}}{9} + \frac{x}{3} + \frac{\log{\left(\sqrt{x} + 3 x + 3 \right)}}{27} + \frac{34 \sqrt{35} \operatorname{atan}{\left(\frac{6 \sqrt{35} \left(\sqrt{x} + \frac{1}{6}\right)}{35} \right)}}{945}$$
Gráfica
Respuesta
[src]
/ ____ ____\ / ____ _____\
____ |\/ 35 6*\/ 21 | ____ |\/ 35 12*\/ 210 |
___ / ____\ / ___\ ____ 34*\/ 35 *atan|------ + --------| 34*\/ 35 *atan|------ + ----------|
4*\/ 6 log\576 + 12*\/ 15 / log\900 + 24*\/ 6 / 2*\/ 15 \ 35 7 / \ 35 35 /
3 - ------- - -------------------- + ------------------- + -------- - --------------------------------- + -----------------------------------
9 27 27 9 945 945
$$- \frac{4 \sqrt{6}}{9} - \frac{34 \sqrt{35} \operatorname{atan}{\left(\frac{\sqrt{35}}{35} + \frac{6 \sqrt{21}}{7} \right)}}{945} - \frac{\log{\left(12 \sqrt{15} + 576 \right)}}{27} + \frac{\log{\left(24 \sqrt{6} + 900 \right)}}{27} + \frac{34 \sqrt{35} \operatorname{atan}{\left(\frac{\sqrt{35}}{35} + \frac{12 \sqrt{210}}{35} \right)}}{945} + \frac{2 \sqrt{15}}{9} + 3$$
=
=
/ ____ ____\ / ____ _____\
____ |\/ 35 6*\/ 21 | ____ |\/ 35 12*\/ 210 |
___ / ____\ / ___\ ____ 34*\/ 35 *atan|------ + --------| 34*\/ 35 *atan|------ + ----------|
4*\/ 6 log\576 + 12*\/ 15 / log\900 + 24*\/ 6 / 2*\/ 15 \ 35 7 / \ 35 35 /
3 - ------- - -------------------- + ------------------- + -------- - --------------------------------- + -----------------------------------
9 27 27 9 945 945
$$- \frac{4 \sqrt{6}}{9} - \frac{34 \sqrt{35} \operatorname{atan}{\left(\frac{\sqrt{35}}{35} + \frac{6 \sqrt{21}}{7} \right)}}{945} - \frac{\log{\left(12 \sqrt{15} + 576 \right)}}{27} + \frac{\log{\left(24 \sqrt{6} + 900 \right)}}{27} + \frac{34 \sqrt{35} \operatorname{atan}{\left(\frac{\sqrt{35}}{35} + \frac{12 \sqrt{210}}{35} \right)}}{945} + \frac{2 \sqrt{15}}{9} + 3$$
3 - 4*sqrt(6)/9 - log(576 + 12*sqrt(15))/27 + log(900 + 24*sqrt(6))/27 + 2*sqrt(15)/9 - 34*sqrt(35)*atan(sqrt(35)/35 + 6*sqrt(21)/7)/945 + 34*sqrt(35)*atan(sqrt(35)/35 + 12*sqrt(210)/35)/945
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.