Sr Examen
Integral de x^4*(ln(4+x^4)-ln(4)) dx
Solución
Ha introducido
[src]
0 / | | 4 / / 4\ \ | x *\log\4 + x / - log(4)/ dx | / -1
$$\int\limits_{-1}^{0} x^{4} \left(\log{\left(x^{4} + 4 \right)} - \log{\left(4 \right)}\right)\, dx$$
Integral(x^4*(log(4 + x^4) - log(4)), (x, -1, 0))
Respuesta (Indefinida)
[src]
/ | / 2 \ 5 / 2 \ 5 5 / 4\ | 4 / / 4\ \ 8*atan(1 + x) 8*atan(-1 + x) 4*log\2 + x + 2*x/ 4*x 4*log\2 + x - 2*x/ 16*x 2*x *log(2) x *log\4 + x / | x *\log\4 + x / - log(4)/ dx = C - ------------- - -------------- - ------------------- - ---- + ------------------- + ---- - ----------- + -------------- | 5 5 5 25 5 5 5 5 /
$$\int x^{4} \left(\log{\left(x^{4} + 4 \right)} - \log{\left(4 \right)}\right)\, dx = C + \frac{x^{5} \log{\left(x^{4} + 4 \right)}}{5} - \frac{2 x^{5} \log{\left(2 \right)}}{5} - \frac{4 x^{5}}{25} + \frac{16 x}{5} + \frac{4 \log{\left(x^{2} - 2 x + 2 \right)}}{5} - \frac{4 \log{\left(x^{2} + 2 x + 2 \right)}}{5} - \frac{8 \operatorname{atan}{\left(x - 1 \right)}}{5} - \frac{8 \operatorname{atan}{\left(x + 1 \right)}}{5}$$
Gráfica
Respuesta
[src]
76 8*atan(2) 3*log(5) 2*log(2) -- - --------- - -------- - -------- 25 5 5 5
$$- \frac{8 \operatorname{atan}{\left(2 \right)}}{5} - \frac{3 \log{\left(5 \right)}}{5} - \frac{2 \log{\left(2 \right)}}{5} + \frac{76}{25}$$
=
=
76 8*atan(2) 3*log(5) 2*log(2) -- - --------- - -------- - -------- 25 5 5 5
$$- \frac{8 \operatorname{atan}{\left(2 \right)}}{5} - \frac{3 \log{\left(5 \right)}}{5} - \frac{2 \log{\left(2 \right)}}{5} + \frac{76}{25}$$
76/25 - 8*atan(2)/5 - 3*log(5)/5 - 2*log(2)/5
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.