Sr Examen
Integral de p/(1+x^3) dx
Solución
Ha introducido
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n / | | p | ------ dx | 3 | 1 + x | / 0
$$\int\limits_{0}^{n} \frac{p}{x^{3} + 1}\, dx$$
Integral(p/(1 + x^3), (x, 0, n))
Respuesta (Indefinida)
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/ / ___ \\ / | ___ |2*\/ 3 *(-1/2 + x)|| | | / 2 \ \/ 3 *atan|------------------|| | p | log\1 + x - x/ log(1 + x) \ 3 /| | ------ dx = C + p*|- --------------- + ---------- + ------------------------------| | 3 \ 6 3 3 / | 1 + x | /
$$\int \frac{p}{x^{3} + 1}\, dx = C + p \left(\frac{\log{\left(x + 1 \right)}}{3} - \frac{\log{\left(x^{2} - x + 1 \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(x - \frac{1}{2}\right)}{3} \right)}}{3}\right)$$
Respuesta
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/ / ___ ___\\ | ___ | \/ 3 2*n*\/ 3 || | / 2 \ \/ 3 *atan|- ----- + ---------|| ___ | log\1 + n - n/ log(1 + n) \ 3 3 /| pi*p*\/ 3 p*|- --------------- + ---------- + -------------------------------| + ---------- \ 6 3 3 / 18
$$p \left(\frac{\log{\left(n + 1 \right)}}{3} - \frac{\log{\left(n^{2} - n + 1 \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} n}{3} - \frac{\sqrt{3}}{3} \right)}}{3}\right) + \frac{\sqrt{3} \pi p}{18}$$
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/ / ___ ___\\ | ___ | \/ 3 2*n*\/ 3 || | / 2 \ \/ 3 *atan|- ----- + ---------|| ___ | log\1 + n - n/ log(1 + n) \ 3 3 /| pi*p*\/ 3 p*|- --------------- + ---------- + -------------------------------| + ---------- \ 6 3 3 / 18
$$p \left(\frac{\log{\left(n + 1 \right)}}{3} - \frac{\log{\left(n^{2} - n + 1 \right)}}{6} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} n}{3} - \frac{\sqrt{3}}{3} \right)}}{3}\right) + \frac{\sqrt{3} \pi p}{18}$$
p*(-log(1 + n^2 - n)/6 + log(1 + n)/3 + sqrt(3)*atan(-sqrt(3)/3 + 2*n*sqrt(3)/3)/3) + pi*p*sqrt(3)/18
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.