Sr Examen
Integral de dx/(3sinx+cosx) dx
Solución
Ha introducido
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1 / | | 1 | ----------------- dx | 3*sin(x) + cos(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{3 \sin{\left(x \right)} + \cos{\left(x \right)}}\, dx$$
Integral(1/(3*sin(x) + cos(x)), (x, 0, 1))
Respuesta (Indefinida)
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/ ____ / ____ /x\\ ____ / ____ /x\\ | \/ 10 *log|-3 - \/ 10 + tan|-|| \/ 10 *log|-3 + \/ 10 + tan|-|| | 1 \ \2// \ \2// | ----------------- dx = C - -------------------------------- + -------------------------------- | 3*sin(x) + cos(x) 10 10 | /
$$\int \frac{1}{3 \sin{\left(x \right)} + \cos{\left(x \right)}}\, dx = C + \frac{\sqrt{10} \log{\left(\tan{\left(\frac{x}{2} \right)} - 3 + \sqrt{10} \right)}}{10} - \frac{\sqrt{10} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{10} - 3 \right)}}{10}$$
Gráfica
Respuesta
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____ / / ____ \\ ____ / ____\ ____ / / ____\\ ____ / ____ \
\/ 10 *\pi*I + log\3 + \/ 10 - tan(1/2)// \/ 10 *log\-3 + \/ 10 / \/ 10 *\pi*I + log\3 + \/ 10 // \/ 10 *log\-3 + \/ 10 + tan(1/2)/
- ------------------------------------------ - ----------------------- + ------------------------------- + ----------------------------------
10 10 10 10
$$\frac{\sqrt{10} \log{\left(-3 + \tan{\left(\frac{1}{2} \right)} + \sqrt{10} \right)}}{10} - \frac{\sqrt{10} \log{\left(-3 + \sqrt{10} \right)}}{10} - \frac{\sqrt{10} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + 3 + \sqrt{10} \right)} + i \pi\right)}{10} + \frac{\sqrt{10} \left(\log{\left(3 + \sqrt{10} \right)} + i \pi\right)}{10}$$
=
=
____ / / ____ \\ ____ / ____\ ____ / / ____\\ ____ / ____ \
\/ 10 *\pi*I + log\3 + \/ 10 - tan(1/2)// \/ 10 *log\-3 + \/ 10 / \/ 10 *\pi*I + log\3 + \/ 10 // \/ 10 *log\-3 + \/ 10 + tan(1/2)/
- ------------------------------------------ - ----------------------- + ------------------------------- + ----------------------------------
10 10 10 10
$$\frac{\sqrt{10} \log{\left(-3 + \tan{\left(\frac{1}{2} \right)} + \sqrt{10} \right)}}{10} - \frac{\sqrt{10} \log{\left(-3 + \sqrt{10} \right)}}{10} - \frac{\sqrt{10} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + 3 + \sqrt{10} \right)} + i \pi\right)}{10} + \frac{\sqrt{10} \left(\log{\left(3 + \sqrt{10} \right)} + i \pi\right)}{10}$$
-sqrt(10)*(pi*i + log(3 + sqrt(10) - tan(1/2)))/10 - sqrt(10)*log(-3 + sqrt(10))/10 + sqrt(10)*(pi*i + log(3 + sqrt(10)))/10 + sqrt(10)*log(-3 + sqrt(10) + tan(1/2))/10
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.