Sr Examen
Integral de 1/(1+3sinxcosx) dx
Solución
Ha introducido
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1 / | | 1 | ------------------- dx | 1 + 3*sin(x)*cos(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{3 \sin{\left(x \right)} \cos{\left(x \right)} + 1}\, dx$$
Integral(1/(1 + (3*sin(x))*cos(x)), (x, 0, 1))
Respuesta (Indefinida)
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/ / ___ | 3 \/ 5 \/ 6 *\/ 3 - \/ 5 /x\| / ___ | 3 \/ 5 \/ 6 *\/ 3 - \/ 5 /x\| ___ | 3 \/ 5 \/ 6 *\/ 3 - \/ 5 /x\| ___ | 3 \/ 5 \/ 6 *\/ 3 - \/ 5 /x\| ____ | 3 \/ 5 \/ 6 *\/ 3 + \/ 5 /x\| ____ | 3 \/ 5 \/ 6 *\/ 3 + \/ 5 /x\| ____ | 3 \/ 5 \/ 6 *\/ 3 - \/ 5 /x\| ____ | 3 \/ 5 \/ 6 *\/ 3 - \/ 5 /x\| ___ | 3 \/ 5 \/ 6 *\/ 3 + \/ 5 /x\| ___ | 3 \/ 5 \/ 6 *\/ 3 + \/ 5 /x\| / ___ | 3 \/ 5 \/ 6 *\/ 3 + \/ 5 /x\| / ___ | 3 \/ 5 \/ 6 *\/ 3 + \/ 5 /x\| ___ / ___ | 3 \/ 5 \/ 6 *\/ 3 + \/ 5 /x\| ___ / ___ | 3 \/ 5 \/ 6 *\/ 3 + \/ 5 /x\| ___ / ___ | 3 \/ 5 \/ 6 *\/ 3 - \/ 5 /x\| ___ / ___ | 3 \/ 5 \/ 6 *\/ 3 - \/ 5 /x\|
| 721827843*\/ 3 + \/ 5 *log|- - + ----- + -------------------- + tan|-|| 721827843*\/ 3 + \/ 5 *log|- - + ----- - -------------------- + tan|-|| 270196287*\/ 6 *log|- - + ----- + -------------------- + tan|-|| 270196287*\/ 6 *log|- - + ----- - -------------------- + tan|-|| 120835453*\/ 30 *log|- - - ----- + -------------------- + tan|-|| 120835453*\/ 30 *log|- - - ----- - -------------------- + tan|-|| 120835453*\/ 30 *log|- - + ----- + -------------------- + tan|-|| 120835453*\/ 30 *log|- - + ----- - -------------------- + tan|-|| 270196287*\/ 6 *log|- - - ----- + -------------------- + tan|-|| 270196287*\/ 6 *log|- - - ----- - -------------------- + tan|-|| 721827843*\/ 3 + \/ 5 *log|- - - ----- + -------------------- + tan|-|| 721827843*\/ 3 + \/ 5 *log|- - - ----- - -------------------- + tan|-|| 322811225*\/ 5 *\/ 3 + \/ 5 *log|- - - ----- + -------------------- + tan|-|| 322811225*\/ 5 *\/ 3 + \/ 5 *log|- - - ----- - -------------------- + tan|-|| 322811225*\/ 5 *\/ 3 + \/ 5 *log|- - + ----- + -------------------- + tan|-|| 322811225*\/ 5 *\/ 3 + \/ 5 *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 - ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------
| 1 + 3*sin(x)*cos(x) ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________
| / ___ ___ ____ ___ / ___ / ___ ___ ____ ___ / ___ / ___ ___ ____ ___ / ___ / ___ ___ ____ ___ / ___ / ___ ___ ____ ___ / ___ / ___ ___ ____ ___ / ___ / ___ ___ ____ ___ / ___ / ___ ___ ____ ___ / ___ / ___ ___ ____ ___ / ___ / ___ ___ ____ ___ / ___ / ___ ___ ____ ___ / ___ / ___ ___ ____ ___ / ___ / ___ ___ ____ ___ / ___ / ___ ___ ____ ___ / ___ / ___ ___ ____ ___ / ___ / ___ ___ ____ ___ / ___
/ - 1614056125*\/ 3 + \/ 5 - 604177265*\/ 6 + 270196287*\/ 30 + 721827843*\/ 5 *\/ 3 + \/ 5 - 1614056125*\/ 3 + \/ 5 - 604177265*\/ 6 + 270196287*\/ 30 + 721827843*\/ 5 *\/ 3 + \/ 5 - 1614056125*\/ 3 + \/ 5 - 604177265*\/ 6 + 270196287*\/ 30 + 721827843*\/ 5 *\/ 3 + \/ 5 - 1614056125*\/ 3 + \/ 5 - 604177265*\/ 6 + 270196287*\/ 30 + 721827843*\/ 5 *\/ 3 + \/ 5 - 1614056125*\/ 3 + \/ 5 - 604177265*\/ 6 + 270196287*\/ 30 + 721827843*\/ 5 *\/ 3 + \/ 5 - 1614056125*\/ 3 + \/ 5 - 604177265*\/ 6 + 270196287*\/ 30 + 721827843*\/ 5 *\/ 3 + \/ 5 - 1614056125*\/ 3 + \/ 5 - 604177265*\/ 6 + 270196287*\/ 30 + 721827843*\/ 5 *\/ 3 + \/ 5 - 1614056125*\/ 3 + \/ 5 - 604177265*\/ 6 + 270196287*\/ 30 + 721827843*\/ 5 *\/ 3 + \/ 5 - 1614056125*\/ 3 + \/ 5 - 604177265*\/ 6 + 270196287*\/ 30 + 721827843*\/ 5 *\/ 3 + \/ 5 - 1614056125*\/ 3 + \/ 5 - 604177265*\/ 6 + 270196287*\/ 30 + 721827843*\/ 5 *\/ 3 + \/ 5 - 1614056125*\/ 3 + \/ 5 - 604177265*\/ 6 + 270196287*\/ 30 + 721827843*\/ 5 *\/ 3 + \/ 5 - 1614056125*\/ 3 + \/ 5 - 604177265*\/ 6 + 270196287*\/ 30 + 721827843*\/ 5 *\/ 3 + \/ 5 - 1614056125*\/ 3 + \/ 5 - 604177265*\/ 6 + 270196287*\/ 30 + 721827843*\/ 5 *\/ 3 + \/ 5 - 1614056125*\/ 3 + \/ 5 - 604177265*\/ 6 + 270196287*\/ 30 + 721827843*\/ 5 *\/ 3 + \/ 5 - 1614056125*\/ 3 + \/ 5 - 604177265*\/ 6 + 270196287*\/ 30 + 721827843*\/ 5 *\/ 3 + \/ 5 - 1614056125*\/ 3 + \/ 5 - 604177265*\/ 6 + 270196287*\/ 30 + 721827843*\/ 5 *\/ 3 + \/ 5
$$\int \frac{1}{3 \sin{\left(x \right)} \cos{\left(x \right)} + 1}\, dx = C - \frac{322811225 \sqrt{5} \sqrt{\sqrt{5} + 3} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{3}{2} - \frac{\sqrt{5}}{2} + \frac{\sqrt{6} \sqrt{\sqrt{5} + 3}}{2} \right)}}{- 1614056125 \sqrt{\sqrt{5} + 3} - 604177265 \sqrt{6} + 270196287 \sqrt{30} + 721827843 \sqrt{5} \sqrt{\sqrt{5} + 3}} - \frac{120835453 \sqrt{30} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{3}{2} - \frac{\sqrt{5}}{2} + \frac{\sqrt{6} \sqrt{\sqrt{5} + 3}}{2} \right)}}{- 1614056125 \sqrt{\sqrt{5} + 3} - 604177265 \sqrt{6} + 270196287 \sqrt{30} + 721827843 \sqrt{5} \sqrt{\sqrt{5} + 3}} + \frac{270196287 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{3}{2} - \frac{\sqrt{5}}{2} + \frac{\sqrt{6} \sqrt{\sqrt{5} + 3}}{2} \right)}}{- 1614056125 \sqrt{\sqrt{5} + 3} - 604177265 \sqrt{6} + 270196287 \sqrt{30} + 721827843 \sqrt{5} \sqrt{\sqrt{5} + 3}} + \frac{721827843 \sqrt{\sqrt{5} + 3} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{3}{2} - \frac{\sqrt{5}}{2} + \frac{\sqrt{6} \sqrt{\sqrt{5} + 3}}{2} \right)}}{- 1614056125 \sqrt{\sqrt{5} + 3} - 604177265 \sqrt{6} + 270196287 \sqrt{30} + 721827843 \sqrt{5} \sqrt{\sqrt{5} + 3}} - \frac{721827843 \sqrt{\sqrt{5} + 3} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{3}{2} - \frac{\sqrt{6} \sqrt{3 - \sqrt{5}}}{2} + \frac{\sqrt{5}}{2} \right)}}{- 1614056125 \sqrt{\sqrt{5} + 3} - 604177265 \sqrt{6} + 270196287 \sqrt{30} + 721827843 \sqrt{5} \sqrt{\sqrt{5} + 3}} - \frac{270196287 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{3}{2} - \frac{\sqrt{6} \sqrt{3 - \sqrt{5}}}{2} + \frac{\sqrt{5}}{2} \right)}}{- 1614056125 \sqrt{\sqrt{5} + 3} - 604177265 \sqrt{6} + 270196287 \sqrt{30} + 721827843 \sqrt{5} \sqrt{\sqrt{5} + 3}} + \frac{120835453 \sqrt{30} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{3}{2} - \frac{\sqrt{6} \sqrt{3 - \sqrt{5}}}{2} + \frac{\sqrt{5}}{2} \right)}}{- 1614056125 \sqrt{\sqrt{5} + 3} - 604177265 \sqrt{6} + 270196287 \sqrt{30} + 721827843 \sqrt{5} \sqrt{\sqrt{5} + 3}} + \frac{322811225 \sqrt{5} \sqrt{\sqrt{5} + 3} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{3}{2} - \frac{\sqrt{6} \sqrt{3 - \sqrt{5}}}{2} + \frac{\sqrt{5}}{2} \right)}}{- 1614056125 \sqrt{\sqrt{5} + 3} - 604177265 \sqrt{6} + 270196287 \sqrt{30} + 721827843 \sqrt{5} \sqrt{\sqrt{5} + 3}} - \frac{721827843 \sqrt{\sqrt{5} + 3} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{3}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{5}}}{2} + \frac{\sqrt{5}}{2} \right)}}{- 1614056125 \sqrt{\sqrt{5} + 3} - 604177265 \sqrt{6} + 270196287 \sqrt{30} + 721827843 \sqrt{5} \sqrt{\sqrt{5} + 3}} - \frac{270196287 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{3}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{5}}}{2} + \frac{\sqrt{5}}{2} \right)}}{- 1614056125 \sqrt{\sqrt{5} + 3} - 604177265 \sqrt{6} + 270196287 \sqrt{30} + 721827843 \sqrt{5} \sqrt{\sqrt{5} + 3}} + \frac{120835453 \sqrt{30} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{3}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{5}}}{2} + \frac{\sqrt{5}}{2} \right)}}{- 1614056125 \sqrt{\sqrt{5} + 3} - 604177265 \sqrt{6} + 270196287 \sqrt{30} + 721827843 \sqrt{5} \sqrt{\sqrt{5} + 3}} + \frac{322811225 \sqrt{5} \sqrt{\sqrt{5} + 3} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{3}{2} + \frac{\sqrt{6} \sqrt{3 - \sqrt{5}}}{2} + \frac{\sqrt{5}}{2} \right)}}{- 1614056125 \sqrt{\sqrt{5} + 3} - 604177265 \sqrt{6} + 270196287 \sqrt{30} + 721827843 \sqrt{5} \sqrt{\sqrt{5} + 3}} - \frac{322811225 \sqrt{5} \sqrt{\sqrt{5} + 3} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{6} \sqrt{\sqrt{5} + 3}}{2} - \frac{3}{2} - \frac{\sqrt{5}}{2} \right)}}{- 1614056125 \sqrt{\sqrt{5} + 3} - 604177265 \sqrt{6} + 270196287 \sqrt{30} + 721827843 \sqrt{5} \sqrt{\sqrt{5} + 3}} - \frac{120835453 \sqrt{30} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{6} \sqrt{\sqrt{5} + 3}}{2} - \frac{3}{2} - \frac{\sqrt{5}}{2} \right)}}{- 1614056125 \sqrt{\sqrt{5} + 3} - 604177265 \sqrt{6} + 270196287 \sqrt{30} + 721827843 \sqrt{5} \sqrt{\sqrt{5} + 3}} + \frac{270196287 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{6} \sqrt{\sqrt{5} + 3}}{2} - \frac{3}{2} - \frac{\sqrt{5}}{2} \right)}}{- 1614056125 \sqrt{\sqrt{5} + 3} - 604177265 \sqrt{6} + 270196287 \sqrt{30} + 721827843 \sqrt{5} \sqrt{\sqrt{5} + 3}} + \frac{721827843 \sqrt{\sqrt{5} + 3} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{6} \sqrt{\sqrt{5} + 3}}{2} - \frac{3}{2} - \frac{\sqrt{5}}{2} \right)}}{- 1614056125 \sqrt{\sqrt{5} + 3} - 604177265 \sqrt{6} + 270196287 \sqrt{30} + 721827843 \sqrt{5} \sqrt{\sqrt{5} + 3}}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.