Sr Examen
Integral de (d*x)/(2x^2+3x-2) dx
Solución
Ha introducido
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3 / | | d*x | -------------- dx | 2 | 2*x + 3*x - 2 | / 2
$$\int\limits_{2}^{3} \frac{d x}{\left(2 x^{2} + 3 x\right) - 2}\, dx$$
Integral((d*x)/(2*x^2 + 3*x - 2), (x, 2, 3))
Respuesta (Indefinida)
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/ / log(8 + 4*x) log(-2 + 4*x)\ | 3*d*|- ------------ + -------------| / 2 \ | d*x \ 5 5 / d*log\-2 + 2*x + 3*x/ | -------------- dx = C - ------------------------------------ + ---------------------- | 2 4 4 | 2*x + 3*x - 2 | /
$$\int \frac{d x}{\left(2 x^{2} + 3 x\right) - 2}\, dx = C - \frac{3 d \left(\frac{\log{\left(4 x - 2 \right)}}{5} - \frac{\log{\left(4 x + 8 \right)}}{5}\right)}{4} + \frac{d \log{\left(2 x^{2} + 3 x - 2 \right)}}{4}$$
Respuesta
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/log(5/2) 2*log(5)\ /log(3/2) 2*log(4)\ d*|-------- + --------| - d*|-------- + --------| \ 10 5 / \ 10 5 /
$$- d \left(\frac{\log{\left(\frac{3}{2} \right)}}{10} + \frac{2 \log{\left(4 \right)}}{5}\right) + d \left(\frac{\log{\left(\frac{5}{2} \right)}}{10} + \frac{2 \log{\left(5 \right)}}{5}\right)$$
=
=
/log(5/2) 2*log(5)\ /log(3/2) 2*log(4)\ d*|-------- + --------| - d*|-------- + --------| \ 10 5 / \ 10 5 /
$$- d \left(\frac{\log{\left(\frac{3}{2} \right)}}{10} + \frac{2 \log{\left(4 \right)}}{5}\right) + d \left(\frac{\log{\left(\frac{5}{2} \right)}}{10} + \frac{2 \log{\left(5 \right)}}{5}\right)$$
d*(log(5/2)/10 + 2*log(5)/5) - d*(log(3/2)/10 + 2*log(4)/5)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.