Sr Examen
Integral de 1/(3+15*sinx*cosx) dx
Solución
Ha introducido
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1 / | | 1 | -------------------- dx | 3 + 15*sin(x)*cos(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{15 \sin{\left(x \right)} \cos{\left(x \right)} + 3}\, dx$$
Integral(1/(3 + (15*sin(x))*cos(x)), (x, 0, 1))
Respuesta (Indefinida)
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| 50068086157525*\/ 5 + \/ 21 *log|- - - ------ + ---------------------- + tan|-|| 50068086157525*\/ 5 + \/ 21 *log|- - - ------ - ---------------------- + tan|-|| 13176181231225*\/ 10 *log|- - - ------ + ---------------------- + tan|-|| 13176181231225*\/ 10 *log|- - - ------ - ---------------------- + tan|-|| 2875278469645*\/ 210 *log|- - + ------ + ---------------------- + tan|-|| 2875278469645*\/ 210 *log|- - + ------ - ---------------------- + tan|-|| 2875278469645*\/ 210 *log|- - - ------ + ---------------------- + tan|-|| 2875278469645*\/ 210 *log|- - - ------ - ---------------------- + tan|-|| 13176181231225*\/ 10 *log|- - + ------ + ---------------------- + tan|-|| 13176181231225*\/ 10 *log|- - + ------ - ---------------------- + tan|-|| 50068086157525*\/ 5 + \/ 21 *log|- - + ------ + ---------------------- + tan|-|| 50068086157525*\/ 5 + \/ 21 *log|- - + ------ - ---------------------- + tan|-|| 10925752129449*\/ 21 *\/ 5 + \/ 21 *log|- - + ------ + ---------------------- + tan|-|| 10925752129449*\/ 21 *\/ 5 + \/ 21 *log|- - + ------ - ---------------------- + tan|-|| 10925752129449*\/ 21 *\/ 5 + \/ 21 *log|- - - ------ + ---------------------- + tan|-|| 10925752129449*\/ 21 *\/ 5 + \/ 21 *log|- - - ------ - ---------------------- + tan|-||
| 1 \ 2 2 2 \2// \ 2 2 2 \2// \ 2 2 2 \2// \ 2 2 2 \2// \ 2 2 2 \2// \ 2 2 2 \2// \ 2 2 2 \2// \ 2 2 2 \2// \ 2 2 2 \2// \ 2 2 2 \2// \ 2 2 2 \2// \ 2 2 2 \2// \ 2 2 2 \2// \ 2 2 2 \2// \ 2 2 2 \2// \ 2 2 2 \2//
| -------------------- dx = C - ---------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------
| 3 + 15*sin(x)*cos(x) ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________
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/ - 39528543693675*\/ 210 + 181142543587635*\/ 10 + 688322384155287*\/ 5 + \/ 21 - 150204258472575*\/ 21 *\/ 5 + \/ 21 - 39528543693675*\/ 210 + 181142543587635*\/ 10 + 688322384155287*\/ 5 + \/ 21 - 150204258472575*\/ 21 *\/ 5 + \/ 21 - 39528543693675*\/ 210 + 181142543587635*\/ 10 + 688322384155287*\/ 5 + \/ 21 - 150204258472575*\/ 21 *\/ 5 + \/ 21 - 39528543693675*\/ 210 + 181142543587635*\/ 10 + 688322384155287*\/ 5 + \/ 21 - 150204258472575*\/ 21 *\/ 5 + \/ 21 - 39528543693675*\/ 210 + 181142543587635*\/ 10 + 688322384155287*\/ 5 + \/ 21 - 150204258472575*\/ 21 *\/ 5 + \/ 21 - 39528543693675*\/ 210 + 181142543587635*\/ 10 + 688322384155287*\/ 5 + \/ 21 - 150204258472575*\/ 21 *\/ 5 + \/ 21 - 39528543693675*\/ 210 + 181142543587635*\/ 10 + 688322384155287*\/ 5 + \/ 21 - 150204258472575*\/ 21 *\/ 5 + \/ 21 - 39528543693675*\/ 210 + 181142543587635*\/ 10 + 688322384155287*\/ 5 + \/ 21 - 150204258472575*\/ 21 *\/ 5 + \/ 21 - 39528543693675*\/ 210 + 181142543587635*\/ 10 + 688322384155287*\/ 5 + \/ 21 - 150204258472575*\/ 21 *\/ 5 + \/ 21 - 39528543693675*\/ 210 + 181142543587635*\/ 10 + 688322384155287*\/ 5 + \/ 21 - 150204258472575*\/ 21 *\/ 5 + \/ 21 - 39528543693675*\/ 210 + 181142543587635*\/ 10 + 688322384155287*\/ 5 + \/ 21 - 150204258472575*\/ 21 *\/ 5 + \/ 21 - 39528543693675*\/ 210 + 181142543587635*\/ 10 + 688322384155287*\/ 5 + \/ 21 - 150204258472575*\/ 21 *\/ 5 + \/ 21 - 39528543693675*\/ 210 + 181142543587635*\/ 10 + 688322384155287*\/ 5 + \/ 21 - 150204258472575*\/ 21 *\/ 5 + \/ 21 - 39528543693675*\/ 210 + 181142543587635*\/ 10 + 688322384155287*\/ 5 + \/ 21 - 150204258472575*\/ 21 *\/ 5 + \/ 21 - 39528543693675*\/ 210 + 181142543587635*\/ 10 + 688322384155287*\/ 5 + \/ 21 - 150204258472575*\/ 21 *\/ 5 + \/ 21 - 39528543693675*\/ 210 + 181142543587635*\/ 10 + 688322384155287*\/ 5 + \/ 21 - 150204258472575*\/ 21 *\/ 5 + \/ 21
$$\int \frac{1}{15 \sin{\left(x \right)} \cos{\left(x \right)} + 3}\, dx = C + \frac{10925752129449 \sqrt{21} \sqrt{\sqrt{21} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{5}{2} - \frac{\sqrt{21}}{2} + \frac{\sqrt{10} \sqrt{\sqrt{21} + 5}}{2} \right)}}{- 150204258472575 \sqrt{21} \sqrt{\sqrt{21} + 5} - 39528543693675 \sqrt{210} + 181142543587635 \sqrt{10} + 688322384155287 \sqrt{\sqrt{21} + 5}} + \frac{2875278469645 \sqrt{210} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{5}{2} - \frac{\sqrt{21}}{2} + \frac{\sqrt{10} \sqrt{\sqrt{21} + 5}}{2} \right)}}{- 150204258472575 \sqrt{21} \sqrt{\sqrt{21} + 5} - 39528543693675 \sqrt{210} + 181142543587635 \sqrt{10} + 688322384155287 \sqrt{\sqrt{21} + 5}} - \frac{13176181231225 \sqrt{10} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{5}{2} - \frac{\sqrt{21}}{2} + \frac{\sqrt{10} \sqrt{\sqrt{21} + 5}}{2} \right)}}{- 150204258472575 \sqrt{21} \sqrt{\sqrt{21} + 5} - 39528543693675 \sqrt{210} + 181142543587635 \sqrt{10} + 688322384155287 \sqrt{\sqrt{21} + 5}} - \frac{50068086157525 \sqrt{\sqrt{21} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{5}{2} - \frac{\sqrt{21}}{2} + \frac{\sqrt{10} \sqrt{\sqrt{21} + 5}}{2} \right)}}{- 150204258472575 \sqrt{21} \sqrt{\sqrt{21} + 5} - 39528543693675 \sqrt{210} + 181142543587635 \sqrt{10} + 688322384155287 \sqrt{\sqrt{21} + 5}} + \frac{50068086157525 \sqrt{\sqrt{21} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{5}{2} - \frac{\sqrt{10} \sqrt{5 - \sqrt{21}}}{2} + \frac{\sqrt{21}}{2} \right)}}{- 150204258472575 \sqrt{21} \sqrt{\sqrt{21} + 5} - 39528543693675 \sqrt{210} + 181142543587635 \sqrt{10} + 688322384155287 \sqrt{\sqrt{21} + 5}} + \frac{13176181231225 \sqrt{10} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{5}{2} - \frac{\sqrt{10} \sqrt{5 - \sqrt{21}}}{2} + \frac{\sqrt{21}}{2} \right)}}{- 150204258472575 \sqrt{21} \sqrt{\sqrt{21} + 5} - 39528543693675 \sqrt{210} + 181142543587635 \sqrt{10} + 688322384155287 \sqrt{\sqrt{21} + 5}} - \frac{2875278469645 \sqrt{210} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{5}{2} - \frac{\sqrt{10} \sqrt{5 - \sqrt{21}}}{2} + \frac{\sqrt{21}}{2} \right)}}{- 150204258472575 \sqrt{21} \sqrt{\sqrt{21} + 5} - 39528543693675 \sqrt{210} + 181142543587635 \sqrt{10} + 688322384155287 \sqrt{\sqrt{21} + 5}} - \frac{10925752129449 \sqrt{21} \sqrt{\sqrt{21} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{5}{2} - \frac{\sqrt{10} \sqrt{5 - \sqrt{21}}}{2} + \frac{\sqrt{21}}{2} \right)}}{- 150204258472575 \sqrt{21} \sqrt{\sqrt{21} + 5} - 39528543693675 \sqrt{210} + 181142543587635 \sqrt{10} + 688322384155287 \sqrt{\sqrt{21} + 5}} + \frac{50068086157525 \sqrt{\sqrt{21} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{5}{2} + \frac{\sqrt{10} \sqrt{5 - \sqrt{21}}}{2} + \frac{\sqrt{21}}{2} \right)}}{- 150204258472575 \sqrt{21} \sqrt{\sqrt{21} + 5} - 39528543693675 \sqrt{210} + 181142543587635 \sqrt{10} + 688322384155287 \sqrt{\sqrt{21} + 5}} + \frac{13176181231225 \sqrt{10} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{5}{2} + \frac{\sqrt{10} \sqrt{5 - \sqrt{21}}}{2} + \frac{\sqrt{21}}{2} \right)}}{- 150204258472575 \sqrt{21} \sqrt{\sqrt{21} + 5} - 39528543693675 \sqrt{210} + 181142543587635 \sqrt{10} + 688322384155287 \sqrt{\sqrt{21} + 5}} - \frac{2875278469645 \sqrt{210} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{5}{2} + \frac{\sqrt{10} \sqrt{5 - \sqrt{21}}}{2} + \frac{\sqrt{21}}{2} \right)}}{- 150204258472575 \sqrt{21} \sqrt{\sqrt{21} + 5} - 39528543693675 \sqrt{210} + 181142543587635 \sqrt{10} + 688322384155287 \sqrt{\sqrt{21} + 5}} - \frac{10925752129449 \sqrt{21} \sqrt{\sqrt{21} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{5}{2} + \frac{\sqrt{10} \sqrt{5 - \sqrt{21}}}{2} + \frac{\sqrt{21}}{2} \right)}}{- 150204258472575 \sqrt{21} \sqrt{\sqrt{21} + 5} - 39528543693675 \sqrt{210} + 181142543587635 \sqrt{10} + 688322384155287 \sqrt{\sqrt{21} + 5}} + \frac{10925752129449 \sqrt{21} \sqrt{\sqrt{21} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{10} \sqrt{\sqrt{21} + 5}}{2} - \frac{5}{2} - \frac{\sqrt{21}}{2} \right)}}{- 150204258472575 \sqrt{21} \sqrt{\sqrt{21} + 5} - 39528543693675 \sqrt{210} + 181142543587635 \sqrt{10} + 688322384155287 \sqrt{\sqrt{21} + 5}} + \frac{2875278469645 \sqrt{210} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{10} \sqrt{\sqrt{21} + 5}}{2} - \frac{5}{2} - \frac{\sqrt{21}}{2} \right)}}{- 150204258472575 \sqrt{21} \sqrt{\sqrt{21} + 5} - 39528543693675 \sqrt{210} + 181142543587635 \sqrt{10} + 688322384155287 \sqrt{\sqrt{21} + 5}} - \frac{13176181231225 \sqrt{10} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{10} \sqrt{\sqrt{21} + 5}}{2} - \frac{5}{2} - \frac{\sqrt{21}}{2} \right)}}{- 150204258472575 \sqrt{21} \sqrt{\sqrt{21} + 5} - 39528543693675 \sqrt{210} + 181142543587635 \sqrt{10} + 688322384155287 \sqrt{\sqrt{21} + 5}} - \frac{50068086157525 \sqrt{\sqrt{21} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{10} \sqrt{\sqrt{21} + 5}}{2} - \frac{5}{2} - \frac{\sqrt{21}}{2} \right)}}{- 150204258472575 \sqrt{21} \sqrt{\sqrt{21} + 5} - 39528543693675 \sqrt{210} + 181142543587635 \sqrt{10} + 688322384155287 \sqrt{\sqrt{21} + 5}}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.