Sr Examen
Integral de dx/(2*x+sqrt(3)*sqrt(x)+1) dx
Solución
Ha introducido
[src]
5 / | | 1 | --------------------- dx | ___ ___ | 2*x + \/ 3 *\/ x + 1 | / 0
$$\int\limits_{0}^{5} \frac{1}{\left(\sqrt{3} \sqrt{x} + 2 x\right) + 1}\, dx$$
Integral(1/(2*x + sqrt(3)*sqrt(x) + 1), (x, 0, 5))
Respuesta (Indefinida)
[src]
/ / ___\\
| ___ | ___ \/ 3 ||
|4*\/ 5 *|\/ x + -----||
/ ____ | \ 4 /|
| / ___ ___\ \/ 15 *atan|-----------------------|
| 1 log\1 + 2*x + \/ 3 *\/ x / \ 5 /
| --------------------- dx = C + -------------------------- - ------------------------------------
| ___ ___ 2 5
| 2*x + \/ 3 *\/ x + 1
|
/
$$\int \frac{1}{\left(\sqrt{3} \sqrt{x} + 2 x\right) + 1}\, dx = C + \frac{\log{\left(\sqrt{3} \sqrt{x} + 2 x + 1 \right)}}{2} - \frac{\sqrt{15} \operatorname{atan}{\left(\frac{4 \sqrt{5} \left(\sqrt{x} + \frac{\sqrt{3}}{4}\right)}{5} \right)}}{5}$$
Gráfica
Respuesta
[src]
/ ____\ / ____\
____ | \/ 15 | ____ |\/ 15 |
/ ____\ \/ 15 *atan|4 + ------| \/ 15 *atan|------|
log\88 + 8*\/ 15 / log(8) \ 5 / \ 5 /
------------------ - ------ - ----------------------- + -------------------
2 2 5 5
$$- \frac{\sqrt{15} \operatorname{atan}{\left(\frac{\sqrt{15}}{5} + 4 \right)}}{5} - \frac{\log{\left(8 \right)}}{2} + \frac{\sqrt{15} \operatorname{atan}{\left(\frac{\sqrt{15}}{5} \right)}}{5} + \frac{\log{\left(8 \sqrt{15} + 88 \right)}}{2}$$
=
=
/ ____\ / ____\
____ | \/ 15 | ____ |\/ 15 |
/ ____\ \/ 15 *atan|4 + ------| \/ 15 *atan|------|
log\88 + 8*\/ 15 / log(8) \ 5 / \ 5 /
------------------ - ------ - ----------------------- + -------------------
2 2 5 5
$$- \frac{\sqrt{15} \operatorname{atan}{\left(\frac{\sqrt{15}}{5} + 4 \right)}}{5} - \frac{\log{\left(8 \right)}}{2} + \frac{\sqrt{15} \operatorname{atan}{\left(\frac{\sqrt{15}}{5} \right)}}{5} + \frac{\log{\left(8 \sqrt{15} + 88 \right)}}{2}$$
log(88 + 8*sqrt(15))/2 - log(8)/2 - sqrt(15)*atan(4 + sqrt(15)/5)/5 + sqrt(15)*atan(sqrt(15)/5)/5
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.