Sr Examen

Otras calculadoras

Resolución de integrales/ x^2+2/ (2x-3)/ (2x-3)/(x^2+2x-7)

Integral de (2x-3)/(x^2+2x-7) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |    2*x - 3      
 |  ------------ dx
 |   2             
 |  x  + 2*x - 7   
 |                 
/                  
0
∫012x−3(x2+2x)−7 dx\int\limits_{0}^{1} \frac{2 x - 3}{\left(x^{2} + 2 x\right) - 7}\, dx 
Integral((2*x - 3)/(x^2 + 2*x - 7), (x, 0, 1))
Respuesta (Indefinida) [src] 
                           //            /  ___        \                   \                     
                           ||   ___      |\/ 2 *(1 + x)|                   |                     
                           ||-\/ 2 *acoth|-------------|                   |                     
  /                        ||            \      4      /              2    |                     
 |                         ||----------------------------  for (1 + x)  > 8|                     
 |   2*x - 3               ||             4                                |      /      2      \
 | ------------ dx = C - 5*|<                                              | + log\-7 + x  + 2*x/
 |  2                      ||            /  ___        \                   |                     
 | x  + 2*x - 7            ||   ___      |\/ 2 *(1 + x)|                   |                     
 |                         ||-\/ 2 *atanh|-------------|                   |                     
/                          ||            \      4      /              2    |                     
                           ||----------------------------  for (1 + x)  < 8|                     
                           \\             4                                /
∫2x−3(x2+2x)−7 dx=C−5({−2acoth⁡(2(x+1)4)4for (x+1)2>8−2atanh⁡(2(x+1)4)4for (x+1)2<8)+log⁡(x2+2x−7)\int \frac{2 x - 3}{\left(x^{2} + 2 x\right) - 7}\, dx = C - 5 \left(\begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} \left(x + 1\right)}{4} \right)}}{4} & \text{for}\: \left(x + 1\right)^{2} > 8 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} \left(x + 1\right)}{4} \right)}}{4} & \text{for}\: \left(x + 1\right)^{2} < 8 \end{cases}\right) + \log{\left(x^{2} + 2 x - 7 \right)}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.20.6
Trazar el gráfico f(x)
Respuesta [src] 
/        ___\                              /        ___\                    /        ___\                              /        ___\                 
|    5*\/ 2 | /          /         ___\\   |    5*\/ 2 |    /        ___\   |    5*\/ 2 | /          /         ___\\   |    5*\/ 2 |    /        ___\
|1 - -------|*\pi*I + log\-2 + 2*\/ 2 // + |1 + -------|*log\2 + 2*\/ 2 / - |1 - -------|*\pi*I + log\-1 + 2*\/ 2 // - |1 + -------|*log\1 + 2*\/ 2 /
\       8   /                              \       8   /                    \       8   /                              \       8   /
−(528+1)log⁡(1+22)+(528+1)log⁡(2+22)−(1−528)(log⁡(−1+22)+iπ)+(1−528)(log⁡(−2+22)+iπ)- \left(\frac{5 \sqrt{2}}{8} + 1\right) \log{\left(1 + 2 \sqrt{2} \right)} + \left(\frac{5 \sqrt{2}}{8} + 1\right) \log{\left(2 + 2 \sqrt{2} \right)} - \left(1 - \frac{5 \sqrt{2}}{8}\right) \left(\log{\left(-1 + 2 \sqrt{2} \right)} + i \pi\right) + \left(1 - \frac{5 \sqrt{2}}{8}\right) \left(\log{\left(-2 + 2 \sqrt{2} \right)} + i \pi\right) 
=
= 
/        ___\                              /        ___\                    /        ___\                              /        ___\                 
|    5*\/ 2 | /          /         ___\\   |    5*\/ 2 |    /        ___\   |    5*\/ 2 | /          /         ___\\   |    5*\/ 2 |    /        ___\
|1 - -------|*\pi*I + log\-2 + 2*\/ 2 // + |1 + -------|*log\2 + 2*\/ 2 / - |1 - -------|*\pi*I + log\-1 + 2*\/ 2 // - |1 + -------|*log\1 + 2*\/ 2 /
\       8   /                              \       8   /                    \       8   /                              \       8   /
−(528+1)log⁡(1+22)+(528+1)log⁡(2+22)−(1−528)(log⁡(−1+22)+iπ)+(1−528)(log⁡(−2+22)+iπ)- \left(\frac{5 \sqrt{2}}{8} + 1\right) \log{\left(1 + 2 \sqrt{2} \right)} + \left(\frac{5 \sqrt{2}}{8} + 1\right) \log{\left(2 + 2 \sqrt{2} \right)} - \left(1 - \frac{5 \sqrt{2}}{8}\right) \left(\log{\left(-1 + 2 \sqrt{2} \right)} + i \pi\right) + \left(1 - \frac{5 \sqrt{2}}{8}\right) \left(\log{\left(-2 + 2 \sqrt{2} \right)} + i \pi\right) 
(1 - 5*sqrt(2)/8)*(pi*i + log(-2 + 2*sqrt(2))) + (1 + 5*sqrt(2)/8)*log(2 + 2*sqrt(2)) - (1 - 5*sqrt(2)/8)*(pi*i + log(-1 + 2*sqrt(2))) - (1 + 5*sqrt(2)/8)*log(1 + 2*sqrt(2))
Respuesta numérica [src] 
0.345259240689554
0.345259240689554

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

    © Sr Examen – Калькулятор