Sr Examen
Integral de (3x-1)/(3+(4x-3)^(-2/4)) dx
Solución
Ha introducido
[src]
1 / | | 3*x - 1 | --------------- dx | 1 | 3 + ----------- | _________ | \/ 4*x - 3 | / 0
$$\int\limits_{0}^{1} \frac{3 x - 1}{3 + \frac{1}{\sqrt{4 x - 3}}}\, dx$$
Integral((3*x - 1)/(3 + 1/sqrt(4*x - 3)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ 1 \ / 1 \ / 2*log|-----------| 2*log|3 + -----------| | _________ | _________| 3/2 2 | _________| | 3*x - 1 1 2*\/ 4*x - 3 \\/ 4*x - 3 / (4*x - 3) (4*x - 3) \ \/ 4*x - 3 / 4*x | --------------- dx = - - + C - ------------- - ------------------ - ------------ + ---------- + ---------------------- + --- | 1 3 27 81 72 32 81 9 | 3 + ----------- | _________ | \/ 4*x - 3 | /
$$\int \frac{3 x - 1}{3 + \frac{1}{\sqrt{4 x - 3}}}\, dx = C + \frac{4 x}{9} - \frac{\left(4 x - 3\right)^{\frac{3}{2}}}{72} - \frac{2 \sqrt{4 x - 3}}{27} + \frac{\left(4 x - 3\right)^{2}}{32} + \frac{2 \log{\left(3 + \frac{1}{\sqrt{4 x - 3}} \right)}}{81} - \frac{2 \log{\left(\frac{1}{\sqrt{4 x - 3}} \right)}}{81} - \frac{1}{3}$$
Gráfica
Respuesta
[src]
/ ___\ / ___\
| I*\/ 3 | |\/ 3 |
2*log|3 - -------| 2*log|-----| ___
23 \ 3 / 2*log(4) \ 3 / pi*I 7*I*\/ 3
--- - ------------------ + -------- + ------------ - ---- + ---------
216 81 81 81 81 216
$$\frac{2 \log{\left(\frac{\sqrt{3}}{3} \right)}}{81} + \frac{2 \log{\left(4 \right)}}{81} + \frac{23}{216} - \frac{i \pi}{81} - \frac{2 \log{\left(3 - \frac{\sqrt{3} i}{3} \right)}}{81} + \frac{7 \sqrt{3} i}{216}$$
=
=
/ ___\ / ___\
| I*\/ 3 | |\/ 3 |
2*log|3 - -------| 2*log|-----| ___
23 \ 3 / 2*log(4) \ 3 / pi*I 7*I*\/ 3
--- - ------------------ + -------- + ------------ - ---- + ---------
216 81 81 81 81 216
$$\frac{2 \log{\left(\frac{\sqrt{3}}{3} \right)}}{81} + \frac{2 \log{\left(4 \right)}}{81} + \frac{23}{216} - \frac{i \pi}{81} - \frac{2 \log{\left(3 - \frac{\sqrt{3} i}{3} \right)}}{81} + \frac{7 \sqrt{3} i}{216}$$
23/216 - 2*log(3 - i*sqrt(3)/3)/81 + 2*log(4)/81 + 2*log(sqrt(3)/3)/81 - pi*i/81 + 7*i*sqrt(3)/216
Respuesta numérica
[src]
(0.0995031359508331 + 0.0216411956499362j)
(0.0995031359508331 + 0.0216411956499362j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.