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Resolución de integrales/ log3x²sec6xdx

Integral de log3x²sec6xdx dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
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∫01log⁡(3x)2sec⁡(6x) dx\int\limits_{0}^{1} \log{\left(3 x \right)}^{2} \sec{\left(6 x \right)}\, dx 
Integral(log(3*x)^2*sec(6*x), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                 /    /                                                             \                                                                   
                                 |   |                                                              |                                                                   
                                 |   | log(sec(6*x) + tan(6*x))                                     |                                                                   
                                 |   | ------------------------ dx                                  |                                                                   
  /                              |   |            x                                                 |                                               /                   
 |                               |   |                                                              |             2                                |                    
 |    2                          |  /                                log(x)*log(sec(6*x) + tan(6*x))|          log (3)*log(sec(6*x) + tan(6*x))    |    2               
 | log (3*x)*sec(6*x) dx = C + 2*|- ------------------------------ + -------------------------------|*log(3) + -------------------------------- +  | log (x)*sec(6*x) dx
 |                               \                6                                 6               /                         6                    |                    
/                                                                                                                                                 /
∫log⁡(3x)2sec⁡(6x) dx=C+2(log⁡(x)log⁡(tan⁡(6x)+sec⁡(6x))6−∫log⁡(tan⁡(6x)+sec⁡(6x))x dx6)log⁡(3)+log⁡(3)2log⁡(tan⁡(6x)+sec⁡(6x))6+∫log⁡(x)2sec⁡(6x) dx\int \log{\left(3 x \right)}^{2} \sec{\left(6 x \right)}\, dx = C + 2 \left(\frac{\log{\left(x \right)} \log{\left(\tan{\left(6 x \right)} + \sec{\left(6 x \right)} \right)}}{6} - \frac{\int \frac{\log{\left(\tan{\left(6 x \right)} + \sec{\left(6 x \right)} \right)}}{x}\, dx}{6}\right) \log{\left(3 \right)} + \frac{\log{\left(3 \right)}^{2} \log{\left(\tan{\left(6 x \right)} + \sec{\left(6 x \right)} \right)}}{6} + \int \log{\left(x \right)}^{2} \sec{\left(6 x \right)}\, dx
Simplificar
Respuesta numérica [src] 
1.26865762613498
1.26865762613498

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

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