Sr Examen

Otras calculadoras

Resolución de integrales/ 3sinx/ xcosx/ cosx+1/ sinxcos/ 1/(3sinxcosx+1)

Integral de 1/(3sinxcosx+1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                       
  /                       
 |                        
 |           1            
 |  ------------------- dx
 |  3*sin(x)*cos(x) + 1   
 |                        
/                         
0
∫0113sin⁡(x)cos⁡(x)+1 dx\int\limits_{0}^{1} \frac{1}{3 \sin{\left(x \right)} \cos{\left(x \right)} + 1}\, dx 
Integral(1/((3*sin(x))*cos(x) + 1), (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 - ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------
 | 3*sin(x)*cos(x) + 1                          ___________                                                           ___________                   ___________                                                           ___________                   ___________                                                           ___________                   ___________                                                           ___________                   ___________                                                           ___________                   ___________                                                           ___________                   ___________                                                           ___________                   ___________                                                           ___________                   ___________                                                           ___________                   ___________                                                           ___________                   ___________                                                           ___________                   ___________                                                           ___________                   ___________                                                           ___________                   ___________                                                           ___________                   ___________                                                           ___________                   ___________                                                           ___________
 |                                             /       ___                ___               ____               ___   /       ___                   /       ___                ___               ____               ___   /       ___                   /       ___                ___               ____               ___   /       ___                   /       ___                ___               ____               ___   /       ___                   /       ___                ___               ____               ___   /       ___                   /       ___                ___               ____               ___   /       ___                   /       ___                ___               ____               ___   /       ___                   /       ___                ___               ____               ___   /       ___                   /       ___                ___               ____               ___   /       ___                   /       ___                ___               ____               ___   /       ___                   /       ___                ___               ____               ___   /       ___                   /       ___                ___               ____               ___   /       ___                   /       ___                ___               ____               ___   /       ___                   /       ___                ___               ____               ___   /       ___                   /       ___                ___               ____               ___   /       ___                   /       ___                ___               ____               ___   /       ___ 
/                               - 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
∫13sin⁡(x)cos⁡(x)+1 dx=C−32281122555+3log⁡(tan⁡(x2)−32−52+65+32)−16140561255+3−6041772656+27019628730+72182784355+3−12083545330log⁡(tan⁡(x2)−32−52+65+32)−16140561255+3−6041772656+27019628730+72182784355+3+2701962876log⁡(tan⁡(x2)−32−52+65+32)−16140561255+3−6041772656+27019628730+72182784355+3+7218278435+3log⁡(tan⁡(x2)−32−52+65+32)−16140561255+3−6041772656+27019628730+72182784355+3−7218278435+3log⁡(tan⁡(x2)−32−63−52+52)−16140561255+3−6041772656+27019628730+72182784355+3−2701962876log⁡(tan⁡(x2)−32−63−52+52)−16140561255+3−6041772656+27019628730+72182784355+3+12083545330log⁡(tan⁡(x2)−32−63−52+52)−16140561255+3−6041772656+27019628730+72182784355+3+32281122555+3log⁡(tan⁡(x2)−32−63−52+52)−16140561255+3−6041772656+27019628730+72182784355+3−7218278435+3log⁡(tan⁡(x2)−32+63−52+52)−16140561255+3−6041772656+27019628730+72182784355+3−2701962876log⁡(tan⁡(x2)−32+63−52+52)−16140561255+3−6041772656+27019628730+72182784355+3+12083545330log⁡(tan⁡(x2)−32+63−52+52)−16140561255+3−6041772656+27019628730+72182784355+3+32281122555+3log⁡(tan⁡(x2)−32+63−52+52)−16140561255+3−6041772656+27019628730+72182784355+3−32281122555+3log⁡(tan⁡(x2)−65+32−32−52)−16140561255+3−6041772656+27019628730+72182784355+3−12083545330log⁡(tan⁡(x2)−65+32−32−52)−16140561255+3−6041772656+27019628730+72182784355+3+2701962876log⁡(tan⁡(x2)−65+32−32−52)−16140561255+3−6041772656+27019628730+72182784355+3+7218278435+3log⁡(tan⁡(x2)−65+32−32−52)−16140561255+3−6041772656+27019628730+72182784355+3\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}}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.902-1
Trazar el gráfico f(x)
Respuesta numérica [src] 
0.517869878725153
0.517869878725153

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

    © Sr Examen – Калькулятор