Sr Examen
Integral de x/(xln^3x) dx
Solución
Ha introducido
[src]
x e / | | x | --------- dx | 3 | x*log (x) | / E
$$\int\limits_{e}^{e^{x}} \frac{x}{x \log{\left(x \right)}^{3}}\, dx$$
Integral(x/((x*log(x)^3)), (x, E, exp(x)))
Respuesta (Indefinida)
[src]
/ | | x li(x) -x - x*log(x) | --------- dx = C + ----- + ------------- | 3 2 2 | x*log (x) 2*log (x) | /
$$\int \frac{x}{x \log{\left(x \right)}^{3}}\, dx = C + \frac{- x \log{\left(x \right)} - x}{2 \log{\left(x \right)}^{2}} + \frac{\operatorname{li}{\left(x \right)}}{2}$$
Respuesta
[src]
/ x\ x x / x\
li\e / li(E) - e - e *log\e /
E + ------ - ----- + -----------------
2 2 2/ x\
2*log \e /
$$\frac{- e^{x} \log{\left(e^{x} \right)} - e^{x}}{2 \log{\left(e^{x} \right)}^{2}} + \frac{\operatorname{li}{\left(e^{x} \right)}}{2} - \frac{\operatorname{li}{\left(e \right)}}{2} + e$$
=
=
/ x\ x x / x\
li\e / li(E) - e - e *log\e /
E + ------ - ----- + -----------------
2 2 2/ x\
2*log \e /
$$\frac{- e^{x} \log{\left(e^{x} \right)} - e^{x}}{2 \log{\left(e^{x} \right)}^{2}} + \frac{\operatorname{li}{\left(e^{x} \right)}}{2} - \frac{\operatorname{li}{\left(e \right)}}{2} + e$$
E + li(exp(x))/2 - li(E)/2 + (-exp(x) - exp(x)*log(exp(x)))/(2*log(exp(x))^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.