Sr Examen
Integral de (4*x+2)/(2*x^2+3)+e*(2*(n+1)^2+3) dx
Solución
Ha introducido
[src]
1 / | | /4*x + 2 / 2 \\ | |-------- + E*\2*(n + 1) + 3/| dx | | 2 | | \2*x + 3 / | / 0
$$\int\limits_{0}^{1} \left(\frac{4 x + 2}{2 x^{2} + 3} + e \left(2 \left(n + 1\right)^{2} + 3\right)\right)\, dx$$
Integral((4*x + 2)/(2*x^2 + 3) + E*(2*(n + 1)^2 + 3), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___\ / ___ |x*\/ 6 | | \/ 6 *atan|-------| | /4*x + 2 / 2 \\ \ 3 / / 2 \ / 2\ | |-------- + E*\2*(n + 1) + 3/| dx = C + ------------------- + E*x*\2*(n + 1) + 3/ + log\3 + 2*x / | | 2 | 3 | \2*x + 3 / | /
$$\int \left(\frac{4 x + 2}{2 x^{2} + 3} + e \left(2 \left(n + 1\right)^{2} + 3\right)\right)\, dx = C + e x \left(2 \left(n + 1\right)^{2} + 3\right) + \log{\left(2 x^{2} + 3 \right)} + \frac{\sqrt{6} \operatorname{atan}{\left(\frac{\sqrt{6} x}{3} \right)}}{3}$$
Respuesta
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/ ___\ / ___\ / ___\ / ___\ / ___\ / / ___\\ / ___\ / / ___\\
| I*\/ 6 | | I*\/ 6 | | I*\/ 6 | | I*\/ 6 | | I*\/ 6 | | pi*I |\/ 6 || | I*\/ 6 | |pi*I |\/ 6 || 2
5*E + |1 - -------|*log|1 - -------| + |1 + -------|*log|1 + -------| - |1 - -------|*|- ---- + log|-----|| - |1 + -------|*|---- + log|-----|| + 2*E*n + 4*E*n
\ 6 / \ 2 / \ 6 / \ 2 / \ 6 / \ 2 \ 2 // \ 6 / \ 2 \ 2 //
$$2 e n^{2} + 4 e n + 5 e - \left(1 + \frac{\sqrt{6} i}{6}\right) \left(\log{\left(\frac{\sqrt{6}}{2} \right)} + \frac{i \pi}{2}\right) + \left(1 - \frac{\sqrt{6} i}{6}\right) \log{\left(1 - \frac{\sqrt{6} i}{2} \right)} + \left(1 + \frac{\sqrt{6} i}{6}\right) \log{\left(1 + \frac{\sqrt{6} i}{2} \right)} - \left(1 - \frac{\sqrt{6} i}{6}\right) \left(\log{\left(\frac{\sqrt{6}}{2} \right)} - \frac{i \pi}{2}\right)$$
=
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/ ___\ / ___\ / ___\ / ___\ / ___\ / / ___\\ / ___\ / / ___\\
| I*\/ 6 | | I*\/ 6 | | I*\/ 6 | | I*\/ 6 | | I*\/ 6 | | pi*I |\/ 6 || | I*\/ 6 | |pi*I |\/ 6 || 2
5*E + |1 - -------|*log|1 - -------| + |1 + -------|*log|1 + -------| - |1 - -------|*|- ---- + log|-----|| - |1 + -------|*|---- + log|-----|| + 2*E*n + 4*E*n
\ 6 / \ 2 / \ 6 / \ 2 / \ 6 / \ 2 \ 2 // \ 6 / \ 2 \ 2 //
$$2 e n^{2} + 4 e n + 5 e - \left(1 + \frac{\sqrt{6} i}{6}\right) \left(\log{\left(\frac{\sqrt{6}}{2} \right)} + \frac{i \pi}{2}\right) + \left(1 - \frac{\sqrt{6} i}{6}\right) \log{\left(1 - \frac{\sqrt{6} i}{2} \right)} + \left(1 + \frac{\sqrt{6} i}{6}\right) \log{\left(1 + \frac{\sqrt{6} i}{2} \right)} - \left(1 - \frac{\sqrt{6} i}{6}\right) \left(\log{\left(\frac{\sqrt{6}}{2} \right)} - \frac{i \pi}{2}\right)$$
5*E + (1 - i*sqrt(6)/6)*log(1 - i*sqrt(6)/2) + (1 + i*sqrt(6)/6)*log(1 + i*sqrt(6)/2) - (1 - i*sqrt(6)/6)*(-pi*i/2 + log(sqrt(6)/2)) - (1 + i*sqrt(6)/6)*(pi*i/2 + log(sqrt(6)/2)) + 2*E*n^2 + 4*E*n
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.