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Resolución de integrales/ asin(bx+90)

Integral de asin(bx+90) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  x                  
  /                  
 |                   
 |  asin(b*x + 90) dx
 |                   
/                    
0
$$\int\limits_{0}^{x} \operatorname{asin}{\left(b x + 90 \right)}\, dx$$ 
Integral(asin(b*x + 90), (x, 0, x))
Respuesta (Indefinida) [src] 
                           //   _________________                                        \
  /                        ||  /               2                                         |
 |                         ||\/  1 - (b*x + 90)   + (b*x + 90)*asin(b*x + 90)            |
 | asin(b*x + 90) dx = C + |<------------------------------------------------  for b != 0|
 |                         ||                       b                                    |
/                          ||                                                            |
                           \\                   x*asin(90)                     otherwise /
$$\int \operatorname{asin}{\left(b x + 90 \right)}\, dx = C + \begin{cases} \frac{\sqrt{1 - \left(b x + 90\right)^{2}} + \left(b x + 90\right) \operatorname{asin}{\left(b x + 90 \right)}}{b} & \text{for}\: b \neq 0 \\x \operatorname{asin}{\left(90 \right)} & \text{otherwise} \end{cases}$$
Simplificar
Respuesta [src] 
/                      _________________________                                                                                 
|                     /          2  2                                                    ______                                  
|                   \/  -8099 - b *x  - 180*b*x    90*asin(90)   90*asin(90 + b*x)   I*\/ 8099                                   
 -oo, b < oo, b != 0)
|                                b                      b                b               b                                       
|                                                                                                                                
\                                          x*asin(90)                                                       otherwise
$$\begin{cases} x \operatorname{asin}{\left(b x + 90 \right)} + \frac{\sqrt{- b^{2} x^{2} - 180 b x - 8099}}{b} + \frac{90 \operatorname{asin}{\left(b x + 90 \right)}}{b} - \frac{\sqrt{8099} i}{b} - \frac{90 \operatorname{asin}{\left(90 \right)}}{b} & \text{for}\: b > -\infty \wedge b < \infty \wedge b \neq 0 \\x \operatorname{asin}{\left(90 \right)} & \text{otherwise} \end{cases}$$ 
=
= 
/                      _________________________                                                                                 
|                     /          2  2                                                    ______                                  
|                   \/  -8099 - b *x  - 180*b*x    90*asin(90)   90*asin(90 + b*x)   I*\/ 8099                                   
 -oo, b < oo, b != 0)
|                                b                      b                b               b                                       
|                                                                                                                                
\                                          x*asin(90)                                                       otherwise
$$\begin{cases} x \operatorname{asin}{\left(b x + 90 \right)} + \frac{\sqrt{- b^{2} x^{2} - 180 b x - 8099}}{b} + \frac{90 \operatorname{asin}{\left(b x + 90 \right)}}{b} - \frac{\sqrt{8099} i}{b} - \frac{90 \operatorname{asin}{\left(90 \right)}}{b} & \text{for}\: b > -\infty \wedge b < \infty \wedge b \neq 0 \\x \operatorname{asin}{\left(90 \right)} & \text{otherwise} \end{cases}$$ 
Piecewise((x*asin(90 + b*x) + sqrt(-8099 - b^2*x^2 - 180*b*x)/b - 90*asin(90)/b + 90*asin(90 + b*x)/b - i*sqrt(8099)/b, (b > -oo)∧(b < oo)∧(Ne(b, 0))), (x*asin(90), True))

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

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