Sr Examen
Integral de x^3*2^x dx
Solución
Ha introducido
[src]
1 / | | 3 x | x *2 dx | / 0
$$\int\limits_{0}^{1} 2^{x} x^{3}\, dx$$
Integral(x^3*2^x, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | x / 3 3 2 2 \ | 3 x 2 *\-6 + x *log (2) - 3*x *log (2) + 6*x*log(2)/ | x *2 dx = C + ------------------------------------------------ | 4 / log (2)
$$\int 2^{x} x^{3}\, dx = \frac{2^{x} \left(x^{3} \log{\left(2 \right)}^{3} - 3 x^{2} \log{\left(2 \right)}^{2} + 6 x \log{\left(2 \right)} - 6\right)}{\log{\left(2 \right)}^{4}} + C$$
Gráfica
Respuesta
[src]
/ 3 2 \ 6 2*\-6 + log (2) - 3*log (2) + 6*log(2)/ ------- + --------------------------------------- 4 4 log (2) log (2)
$$\frac{2 \left(-6 - 3 \log{\left(2 \right)}^{2} + \log{\left(2 \right)}^{3} + 6 \log{\left(2 \right)}\right)}{\log{\left(2 \right)}^{4}} + \frac{6}{\log{\left(2 \right)}^{4}}$$
=
=
/ 3 2 \ 6 2*\-6 + log (2) - 3*log (2) + 6*log(2)/ ------- + --------------------------------------- 4 4 log (2) log (2)
$$\frac{2 \left(-6 - 3 \log{\left(2 \right)}^{2} + \log{\left(2 \right)}^{3} + 6 \log{\left(2 \right)}\right)}{\log{\left(2 \right)}^{4}} + \frac{6}{\log{\left(2 \right)}^{4}}$$
6/log(2)^4 + 2*(-6 + log(2)^3 - 3*log(2)^2 + 6*log(2))/log(2)^4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.