Sr Examen
Integral de 1/(sin(x)^2+3cos(x)sin(x)+cos(x)^2) dx
Solución
Ha introducido
[src]
1 / | | 1 | ----------------------------------- dx | 2 2 | sin (x) + 3*cos(x)*sin(x) + cos (x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(\sin^{2}{\left(x \right)} + \sin{\left(x \right)} 3 \cos{\left(x \right)}\right) + \cos^{2}{\left(x \right)}}\, dx$$
Integral(1/(sin(x)^2 + (3*cos(x))*sin(x) + cos(x)^2), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___________ \ / ___________ \ / ___________ \ / ___________ \ / ___________ \ / ___________ \ / ___________ \ / ___________ \ / ___________ \ / ___________ \ / ___________ \ / ___________ \ / ___________ \ / ___________ \ / ___________ \ / ___________ \
___________ | ___ ___ / ___ | ___________ | ___ ___ / ___ | | ___ ___ / ___ | | ___ ___ / ___ | | ___ ___ / ___ | | ___ ___ / ___ | | ___ ___ / ___ | | ___ ___ / ___ | | ___ ___ / ___ | | ___ ___ / ___ | ___________ | ___ ___ / ___ | ___________ | ___ ___ / ___ | ___________ | ___ ___ / ___ | ___________ | ___ ___ / ___ | ___________ | ___ ___ / ___ | ___________ | ___ ___ / ___ |
/ / ___ | 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 - ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------
| 2 2 ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________
| sin (x) + 3*cos(x)*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}{\left(\sin^{2}{\left(x \right)} + \sin{\left(x \right)} 3 \cos{\left(x \right)}\right) + \cos^{2}{\left(x \right)}}\, 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.