Sr Examen
Integral de (0.1+sqrt(x))/(log((x^2),10)+1) dx
Solución
Ha introducido
[src]
4 / | | 1 ___ | -- + \/ x | 10 | --------------- dx | / 2 \ | log\x , 10/ + 1 | / 2
$$\int\limits_{2}^{4} \frac{\sqrt{x} + \frac{1}{10}}{\log{\left(x^{2} \right)} + 1}\, dx$$
Integral((1/10 + sqrt(x))/(log(x^2, 10) + 1), (x, 2, 4))
Respuesta (Indefinida)
[src]
/ / \
| | |
/ ___ \ | | 1 |
/ | \/ x | | | ----------------- dx|*log(10)
| | / | | | / 2\ |
| 1 ___ | | | | | log(10) + log\x / |
| -- + \/ x | | 2 | | | |
| 10 | | u | \/ /
| --------------- dx = C + 2*| | ----------------- du|*log(10) + ---------------------------------
| / 2 \ | | / 4\ | 10
| log\x , 10/ + 1 | | log(10) + log\u / |
| | | |
/ | / |
\ /
$$\int \frac{\sqrt{x} + \frac{1}{10}}{\log{\left(x^{2} \right)} + 1}\, dx = C + 2 \log{\left(10 \right)} \int\limits^{\sqrt{x}} \frac{u^{2}}{\log{\left(u^{4} \right)} + \log{\left(10 \right)}}\, du + \frac{\log{\left(10 \right)} \int \frac{1}{\log{\left(x^{2} \right)} + \log{\left(10 \right)}}\, dx}{10}$$
Respuesta
[src]
/ 4 \
| 4 / |
| / | |
| | | ___ |
| | 1 | 10*\/ x |
| | ------------------ dx + | ------------------ dx|*log(10)
| | 2*log(x) + log(10) | 2*log(x) + log(10) |
| | | |
|/ / |
\2 2 /
---------------------------------------------------------------
10
$$\frac{\left(\int\limits_{2}^{4} \frac{1}{2 \log{\left(x \right)} + \log{\left(10 \right)}}\, dx + \int\limits_{2}^{4} \frac{10 \sqrt{x}}{2 \log{\left(x \right)} + \log{\left(10 \right)}}\, dx\right) \log{\left(10 \right)}}{10}$$
=
=
/ 4 \
| 4 / |
| / | |
| | | ___ |
| | 1 | 10*\/ x |
| | ------------------ dx + | ------------------ dx|*log(10)
| | 2*log(x) + log(10) | 2*log(x) + log(10) |
| | | |
|/ / |
\2 2 /
---------------------------------------------------------------
10
$$\frac{\left(\int\limits_{2}^{4} \frac{1}{2 \log{\left(x \right)} + \log{\left(10 \right)}}\, dx + \int\limits_{2}^{4} \frac{10 \sqrt{x}}{2 \log{\left(x \right)} + \log{\left(10 \right)}}\, dx\right) \log{\left(10 \right)}}{10}$$
(Integral(1/(2*log(x) + log(10)), (x, 2, 4)) + Integral(10*sqrt(x)/(2*log(x) + log(10)), (x, 2, 4)))*log(10)/10
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.