Sr Examen
Integral de 1/((6x^2-5x+1)*ln(3/4)) dx
Solución
Ha introducido
[src]
oo / | | 1 | ------------------------- dx | / 2 \ | \6*x - 5*x + 1/*log(3/4) | / 1
$$\int\limits_{1}^{\infty} \frac{1}{\left(\left(6 x^{2} - 5 x\right) + 1\right) \log{\left(\frac{3}{4} \right)}}\, dx$$
Integral(1/((6*x^2 - 5*x + 1)*log(3/4)), (x, 1, oo))
Respuesta (Indefinida)
[src]
/ | | 1 -log(-4 + 12*x) + log(-6 + 12*x) | ------------------------- dx = C + -------------------------------- | / 2 \ log(3/4) | \6*x - 5*x + 1/*log(3/4) | /
$$\int \frac{1}{\left(\left(6 x^{2} - 5 x\right) + 1\right) \log{\left(\frac{3}{4} \right)}}\, dx = C + \frac{\log{\left(12 x - 6 \right)} - \log{\left(12 x - 4 \right)}}{\log{\left(\frac{3}{4} \right)}}$$
Gráfica
Respuesta
[src]
/7 log(2) log(3) \ /7 log(3) log(2) \
log|-- - ---------------------- + -----------------------| log|-- - ----------------------- + ----------------------|
\12 6*(-log(3) + 2*log(2)) 12*(-log(3) + 2*log(2))/ \12 12*(-log(3) + 2*log(2)) 6*(-log(3) + 2*log(2))/
---------------------------------------------------------- - ----------------------------------------------------------
-log(3) + 2*log(2) -log(3) + 2*log(2)
$$\frac{\log{\left(- \frac{\log{\left(2 \right)}}{6 \left(- \log{\left(3 \right)} + 2 \log{\left(2 \right)}\right)} + \frac{\log{\left(3 \right)}}{12 \left(- \log{\left(3 \right)} + 2 \log{\left(2 \right)}\right)} + \frac{7}{12} \right)}}{- \log{\left(3 \right)} + 2 \log{\left(2 \right)}} - \frac{\log{\left(- \frac{\log{\left(3 \right)}}{12 \left(- \log{\left(3 \right)} + 2 \log{\left(2 \right)}\right)} + \frac{\log{\left(2 \right)}}{6 \left(- \log{\left(3 \right)} + 2 \log{\left(2 \right)}\right)} + \frac{7}{12} \right)}}{- \log{\left(3 \right)} + 2 \log{\left(2 \right)}}$$
=
=
/7 log(2) log(3) \ /7 log(3) log(2) \
log|-- - ---------------------- + -----------------------| log|-- - ----------------------- + ----------------------|
\12 6*(-log(3) + 2*log(2)) 12*(-log(3) + 2*log(2))/ \12 12*(-log(3) + 2*log(2)) 6*(-log(3) + 2*log(2))/
---------------------------------------------------------- - ----------------------------------------------------------
-log(3) + 2*log(2) -log(3) + 2*log(2)
$$\frac{\log{\left(- \frac{\log{\left(2 \right)}}{6 \left(- \log{\left(3 \right)} + 2 \log{\left(2 \right)}\right)} + \frac{\log{\left(3 \right)}}{12 \left(- \log{\left(3 \right)} + 2 \log{\left(2 \right)}\right)} + \frac{7}{12} \right)}}{- \log{\left(3 \right)} + 2 \log{\left(2 \right)}} - \frac{\log{\left(- \frac{\log{\left(3 \right)}}{12 \left(- \log{\left(3 \right)} + 2 \log{\left(2 \right)}\right)} + \frac{\log{\left(2 \right)}}{6 \left(- \log{\left(3 \right)} + 2 \log{\left(2 \right)}\right)} + \frac{7}{12} \right)}}{- \log{\left(3 \right)} + 2 \log{\left(2 \right)}}$$
log(7/12 - log(2)/(6*(-log(3) + 2*log(2))) + log(3)/(12*(-log(3) + 2*log(2))))/(-log(3) + 2*log(2)) - log(7/12 - log(3)/(12*(-log(3) + 2*log(2))) + log(2)/(6*(-log(3) + 2*log(2))))/(-log(3) + 2*log(2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.