Sr Examen
Integral de Ln(2*x+3)/(4x+3)^1/5 dx
Solución
Ha introducido
[src]
oo / | | log(2*x + 3) | ------------ dx | 5 _________ | \/ 4*x + 3 | / 1
$$\int\limits_{1}^{\infty} \frac{\log{\left(2 x + 3 \right)}}{\sqrt[5]{4 x + 3}}\, dx$$
Integral(log(2*x + 3)/(4*x + 3)^(1/5), (x, 1, oo))
Respuesta (Indefinida)
[src]
/ pi*I\ / 3*pi*I\ / 7*pi*I\ / 9*pi*I\
-4*pi*I | ----| -2*pi*I | ------| 2*pi*I | ------| 4*pi*I | ------|
/ 2/5 4/5 5 _________ pi*I\ ------- | 2/5 4/5 5 _________ 5 | ------- | 2/5 4/5 5 _________ 5 | ------ | 2/5 4/5 5 _________ 5 | ------ | 2/5 4/5 5 _________ 5 |
/ 4/5 | 2 *3 *\/ 3/4 + x *e | 4/5 5 | 2 *3 *\/ 3/4 + x *e | 4/5 5 | 2 *3 *\/ 3/4 + x *e | 4/5 5 | 2 *3 *\/ 3/4 + x *e | 4/5 5 | 2 *3 *\/ 3/4 + x *e |
| 4/5 3/5 4/5 9*3 *Gamma(9/5)*log|1 - ---------------------------| 9*3 *e *Gamma(9/5)*log|1 - ---------------------------| 9*3 *e *Gamma(9/5)*log|1 - -----------------------------| 9*3 *e *Gamma(9/5)*log|1 - -----------------------------| 9*3 *e *Gamma(9/5)*log|1 - -----------------------------|
| log(2*x + 3) 5*(3 + 4*x) *log(2*x + 3) 45*2 *(3/4 + x) *Gamma(9/5) \ 3 / \ 3 / \ 3 / \ 3 / \ 3 /
| ------------ dx = C + --------------------------- - ------------------------------- - ------------------------------------------------------ - --------------------------------------------------------------- - ----------------------------------------------------------------- - ---------------------------------------------------------------- - ----------------------------------------------------------------
| 5 _________ 16 32*Gamma(14/5) 16*Gamma(14/5) 16*Gamma(14/5) 16*Gamma(14/5) 16*Gamma(14/5) 16*Gamma(14/5)
| \/ 4*x + 3
|
/
$$\int \frac{\log{\left(2 x + 3 \right)}}{\sqrt[5]{4 x + 3}}\, dx = C - \frac{45 \cdot 2^{\frac{3}{5}} \left(x + \frac{3}{4}\right)^{\frac{4}{5}} \Gamma\left(\frac{9}{5}\right)}{32 \Gamma\left(\frac{14}{5}\right)} + \frac{5 \left(4 x + 3\right)^{\frac{4}{5}} \log{\left(2 x + 3 \right)}}{16} - \frac{9 \cdot 3^{\frac{4}{5}} e^{- \frac{4 i \pi}{5}} \log{\left(- \frac{2^{\frac{2}{5}} \cdot 3^{\frac{4}{5}} \sqrt[5]{x + \frac{3}{4}} e^{\frac{i \pi}{5}}}{3} + 1 \right)} \Gamma\left(\frac{9}{5}\right)}{16 \Gamma\left(\frac{14}{5}\right)} - \frac{9 \cdot 3^{\frac{4}{5}} e^{- \frac{2 i \pi}{5}} \log{\left(- \frac{2^{\frac{2}{5}} \cdot 3^{\frac{4}{5}} \sqrt[5]{x + \frac{3}{4}} e^{\frac{3 i \pi}{5}}}{3} + 1 \right)} \Gamma\left(\frac{9}{5}\right)}{16 \Gamma\left(\frac{14}{5}\right)} - \frac{9 \cdot 3^{\frac{4}{5}} \log{\left(- \frac{2^{\frac{2}{5}} \cdot 3^{\frac{4}{5}} \sqrt[5]{x + \frac{3}{4}} e^{i \pi}}{3} + 1 \right)} \Gamma\left(\frac{9}{5}\right)}{16 \Gamma\left(\frac{14}{5}\right)} - \frac{9 \cdot 3^{\frac{4}{5}} e^{\frac{2 i \pi}{5}} \log{\left(- \frac{2^{\frac{2}{5}} \cdot 3^{\frac{4}{5}} \sqrt[5]{x + \frac{3}{4}} e^{\frac{7 i \pi}{5}}}{3} + 1 \right)} \Gamma\left(\frac{9}{5}\right)}{16 \Gamma\left(\frac{14}{5}\right)} - \frac{9 \cdot 3^{\frac{4}{5}} e^{\frac{4 i \pi}{5}} \log{\left(- \frac{2^{\frac{2}{5}} \cdot 3^{\frac{4}{5}} \sqrt[5]{x + \frac{3}{4}} e^{\frac{9 i \pi}{5}}}{3} + 1 \right)} \Gamma\left(\frac{9}{5}\right)}{16 \Gamma\left(\frac{14}{5}\right)}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.