Sr Examen
Integral de 1/(cbrt(x)+2)^2 dx
Solución
Ha introducido
[src]
4 / | | 1 | ------------ dx | 2 | /3 ___ \ | \\/ x + 2/ | / 0
$$\int\limits_{0}^{4} \frac{1}{\left(\sqrt[3]{x} + 2\right)^{2}}\, dx$$
Integral(1/((x^(1/3) + 2)^2), (x, 0, 4))
Respuesta (Indefinida)
[src]
/ | | 1 12 / 3 ___\ 3 ___ | ------------ dx = C - --------- - 12*log\2 + \/ x / + 3*\/ x | 2 3 ___ | /3 ___ \ 2 + \/ x | \\/ x + 2/ | /
$$\int \frac{1}{\left(\sqrt[3]{x} + 2\right)^{2}}\, dx = C + 3 \sqrt[3]{x} - 12 \log{\left(\sqrt[3]{x} + 2 \right)} - \frac{12}{\sqrt[3]{x} + 2}$$
Gráfica
Respuesta
[src]
/ 2/3\ 3 ___ 2/3 / 2/3\
24 24*log\2 + 2 / 6*\/ 2 12*2 *log\2 + 2 /
12 - -------- + 12*log(2) - ---------------- + -------- - ---------------------
2/3 2/3 2/3 2/3
2 + 2 2 + 2 2 + 2 2 + 2
$$- \frac{24 \log{\left(2^{\frac{2}{3}} + 2 \right)}}{2^{\frac{2}{3}} + 2} - \frac{12 \cdot 2^{\frac{2}{3}} \log{\left(2^{\frac{2}{3}} + 2 \right)}}{2^{\frac{2}{3}} + 2} - \frac{24}{2^{\frac{2}{3}} + 2} + \frac{6 \sqrt[3]{2}}{2^{\frac{2}{3}} + 2} + 12 \log{\left(2 \right)} + 12$$
=
=
/ 2/3\ 3 ___ 2/3 / 2/3\
24 24*log\2 + 2 / 6*\/ 2 12*2 *log\2 + 2 /
12 - -------- + 12*log(2) - ---------------- + -------- - ---------------------
2/3 2/3 2/3 2/3
2 + 2 2 + 2 2 + 2 2 + 2
$$- \frac{24 \log{\left(2^{\frac{2}{3}} + 2 \right)}}{2^{\frac{2}{3}} + 2} - \frac{12 \cdot 2^{\frac{2}{3}} \log{\left(2^{\frac{2}{3}} + 2 \right)}}{2^{\frac{2}{3}} + 2} - \frac{24}{2^{\frac{2}{3}} + 2} + \frac{6 \sqrt[3]{2}}{2^{\frac{2}{3}} + 2} + 12 \log{\left(2 \right)} + 12$$
12 - 24/(2 + 2^(2/3)) + 12*log(2) - 24*log(2 + 2^(2/3))/(2 + 2^(2/3)) + 6*2^(1/3)/(2 + 2^(2/3)) - 12*2^(2/3)*log(2 + 2^(2/3))/(2 + 2^(2/3))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.