Sr Examen
Integral de 1÷(sinx+cosx) dx
Solución
Ha introducido
[src]
1 / | | 1 | --------------- dx | sin(x) + cos(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)}}\, dx$$
Integral(1/(sin(x) + cos(x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___ / ___ /x\\ ___ / ___ /x\\ | \/ 2 *log|-1 + \/ 2 + tan|-|| \/ 2 *log|-1 - \/ 2 + tan|-|| | 1 \ \2// \ \2// | --------------- dx = C + ------------------------------ - ------------------------------ | sin(x) + cos(x) 2 2 | /
$$\int \frac{1}{\sin{\left(x \right)} + \cos{\left(x \right)}}\, dx = C + \frac{\sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)}}{2} - \frac{\sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)}}{2}$$
Gráfica
Respuesta
[src]
___ / / ___\\ ___ / ___ \ ___ / / ___ \\ ___ / ___\
\/ 2 *\pi*I + log\1 + \/ 2 // \/ 2 *log\-1 + \/ 2 + tan(1/2)/ \/ 2 *\pi*I + log\1 + \/ 2 - tan(1/2)// \/ 2 *log\-1 + \/ 2 /
----------------------------- + -------------------------------- - ---------------------------------------- - ---------------------
2 2 2 2
$$\frac{\sqrt{2} \log{\left(-1 + \tan{\left(\frac{1}{2} \right)} + \sqrt{2} \right)}}{2} - \frac{\sqrt{2} \log{\left(-1 + \sqrt{2} \right)}}{2} - \frac{\sqrt{2} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + 1 + \sqrt{2} \right)} + i \pi\right)}{2} + \frac{\sqrt{2} \left(\log{\left(1 + \sqrt{2} \right)} + i \pi\right)}{2}$$
=
=
___ / / ___\\ ___ / ___ \ ___ / / ___ \\ ___ / ___\
\/ 2 *\pi*I + log\1 + \/ 2 // \/ 2 *log\-1 + \/ 2 + tan(1/2)/ \/ 2 *\pi*I + log\1 + \/ 2 - tan(1/2)// \/ 2 *log\-1 + \/ 2 /
----------------------------- + -------------------------------- - ---------------------------------------- - ---------------------
2 2 2 2
$$\frac{\sqrt{2} \log{\left(-1 + \tan{\left(\frac{1}{2} \right)} + \sqrt{2} \right)}}{2} - \frac{\sqrt{2} \log{\left(-1 + \sqrt{2} \right)}}{2} - \frac{\sqrt{2} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + 1 + \sqrt{2} \right)} + i \pi\right)}{2} + \frac{\sqrt{2} \left(\log{\left(1 + \sqrt{2} \right)} + i \pi\right)}{2}$$
sqrt(2)*(pi*i + log(1 + sqrt(2)))/2 + sqrt(2)*log(-1 + sqrt(2) + tan(1/2))/2 - sqrt(2)*(pi*i + log(1 + sqrt(2) - tan(1/2)))/2 - sqrt(2)*log(-1 + sqrt(2))/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.