Sr Examen
Integral de (exp(0,7*x)+5,57271-4,92858*x)*cos(2,1*p-p*x) dx
Solución
Ha introducido
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21 -- 10 / | | / 7*x \ | | --- | | | 10 | /21*p \ | \e + 5.57271 - 4.92858*x/*cos|---- - p*x| dx | \ 10 / | / 9/10
$$\int\limits_{\frac{9}{10}}^{\frac{21}{10}} \left(- 4.92858 x + \left(e^{\frac{7 x}{10}} + 5.57271\right)\right) \cos{\left(- p x + \frac{21 p}{10} \right)}\, dx$$
Integral((exp(7*x/10) + 5.57271 - 4.92858*x)*cos(21*p/10 - p*x), (x, 9/10, 21/10))
Respuesta (Indefinida)
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/ / // / 7*x 7*x 7*x\ \ \ \
| | || | --- --- ---| | | |
| | || | 10 / 147 7*x\ 10 / 147 7*x\ / 147 7*x\ 10| | | |
| | || |5*e *sinh|- --- + ---| x*e *sinh|- --- + ---| x*cosh|- --- + ---|*e | | | |
| | || | \ 100 10/ \ 100 10/ \ 100 10/ | -7*I| | |
| | ||-I*|------------------------ + ------------------------ - ------------------------| for p = ----| | |
| | || \ 7 2 2 / 10 | | |
| | || | | |
| | || / 7*x 7*x 7*x\ | | |
| | || | --- --- ---| | | |
| | || | 10 / 147 7*x\ 10 / 147 7*x\ / 147 7*x\ 10| | | |
| | || |5*e *sinh|- --- + ---| x*e *sinh|- --- + ---| x*cosh|- --- + ---|*e | | | |
| |10*p*|< | \ 100 10/ \ 100 10/ \ 100 10/ | 7*I | | |
| | ||I*|------------------------ + ------------------------ - ------------------------| for p = --- | | |
| | || \ 7 2 2 / 10 | | |
| | || | | |
| | || 7*x 7*x | | |
| | || --- --- | | |
| | || 10 / 21*p \ / 21*p \ 10 | | |
| | || 70*e *sin|- ---- + p*x| 100*p*cos|- ---- + p*x|*e | | |
| | || \ 10 / \ 10 / | 7*x| |
| | || ------------------------- - ---------------------------- otherwise | ---| |
| | || 2 2 | / 21*p \ 10| 7*x |
| | || 49 + 100*p 49 + 100*p | 10*cos|- ---- + p*x|*e | --- |
/ // 2 \ | | \\ / \ 10 / | 10 / 21*p \| 7*x
| || x | | 10*p*|--------------------------------------------------------------------------------------------------------- + -------------------------| 10*e *sin|- ---- + p*x|| ---
| / 7*x \ || -- for p = 0| // x for p = 0\ | \ 7 7 / \ 10 /| / 21*p \ 10 // x for p = 0\
| | --- | || 2 | || | 10*p*|- -------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------| 10*cos|- ---- + p*x|*e || |
| | 10 | /21*p \ || | || / 21*p \ | \ 7 7 / \ 10 / || /p*(-21 + 10*x)\ |
| \e + 5.57271 - 4.92858*x/*cos|---- - p*x| dx = C + 4.92858*|< / / 21 \\ | + 5.57271*|
$$\int \left(- 4.92858 x + \left(e^{\frac{7 x}{10}} + 5.57271\right)\right) \cos{\left(- p x + \frac{21 p}{10} \right)}\, dx = C + \frac{10 p \left(- \frac{10 p \left(\frac{10 p \left(\begin{cases} - i \left(\frac{x e^{\frac{7 x}{10}} \sinh{\left(\frac{7 x}{10} - \frac{147}{100} \right)}}{2} - \frac{x e^{\frac{7 x}{10}} \cosh{\left(\frac{7 x}{10} - \frac{147}{100} \right)}}{2} + \frac{5 e^{\frac{7 x}{10}} \sinh{\left(\frac{7 x}{10} - \frac{147}{100} \right)}}{7}\right) & \text{for}\: p = - \frac{7 i}{10} \\i \left(\frac{x e^{\frac{7 x}{10}} \sinh{\left(\frac{7 x}{10} - \frac{147}{100} \right)}}{2} - \frac{x e^{\frac{7 x}{10}} \cosh{\left(\frac{7 x}{10} - \frac{147}{100} \right)}}{2} + \frac{5 e^{\frac{7 x}{10}} \sinh{\left(\frac{7 x}{10} - \frac{147}{100} \right)}}{7}\right) & \text{for}\: p = \frac{7 i}{10} \\- \frac{100 p e^{\frac{7 x}{10}} \cos{\left(p x - \frac{21 p}{10} \right)}}{100 p^{2} + 49} + \frac{70 e^{\frac{7 x}{10}} \sin{\left(p x - \frac{21 p}{10} \right)}}{100 p^{2} + 49} & \text{otherwise} \end{cases}\right)}{7} + \frac{10 e^{\frac{7 x}{10}} \cos{\left(p x - \frac{21 p}{10} \right)}}{7}\right)}{7} + \frac{10 e^{\frac{7 x}{10}} \sin{\left(p x - \frac{21 p}{10} \right)}}{7}\right)}{7} - 4.92858 x \left(\begin{cases} x & \text{for}\: p = 0 \\\frac{\sin{\left(\frac{p \left(10 x - 21\right)}{10} \right)}}{p} & \text{otherwise} \end{cases}\right) + 5.57271 \left(\begin{cases} x & \text{for}\: p = 0 \\\frac{\sin{\left(p x - \frac{21 p}{10} \right)}}{p} & \text{otherwise} \end{cases}\right) + 4.92858 \left(\begin{cases} \frac{x^{2}}{2} & \text{for}\: p = 0 \\- \frac{\cos{\left(p \left(x - \frac{21}{10}\right) \right)}}{p^{2}} & \text{otherwise} \end{cases}\right) + \frac{10 e^{\frac{7 x}{10}} \cos{\left(p x - \frac{21 p}{10} \right)}}{7}$$
Respuesta
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/ 147 63 | --- --- | 100 100 | -2.184192 + 1.42857142857143*e - 1.42857142857143*e for p = 0 | | 63 63 63 63 < 147 147 --- --- --- --- | /6*p\ --- --- 4 /6*p\ 2 /6*p\ /6*p\ 3 /6*p\ 5 /6*p\ 5 100 /6*p\ 3 100 /6*p\ 4 /6*p\ 100 2 /6*p\ 100 | 40588975589.4*cos|---| 4 2 4 100 2 100 169050294000.0*p *cos|---| 165669288120.0*p *cos|---| 9363585084.84*p*sin|---| 38218714632.0*p *sin|---| 38998688400.0*p *sin|---| 34300000000.0*p *e *sin|---| 16807000000.0*p *e *sin|---| 24010000000.0*p *cos|---|*e 11764900000.0*p *cos|---|*e | 40588975589.4 \ 5 / 169050294000.0*p 165669288120.0*p 24010000000.0*p *e 11764900000.0*p *e \ 5 / \ 5 / \ 5 / \ 5 / \ 5 / \ 5 / \ 5 / \ 5 / \ 5 / |- ----------------------------------------------------- + ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- otherwise | 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 \ 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p
$$\begin{cases} - 1.42857142857143 e^{\frac{63}{100}} - 2.184192 + 1.42857142857143 e^{\frac{147}{100}} & \text{for}\: p = 0 \\\frac{38998688400.0 p^{5} \sin{\left(\frac{6 p}{5} \right)}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} + \frac{34300000000.0 p^{5} e^{\frac{63}{100}} \sin{\left(\frac{6 p}{5} \right)}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} - \frac{24010000000.0 p^{4} e^{\frac{63}{100}} \cos{\left(\frac{6 p}{5} \right)}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} + \frac{169050294000.0 p^{4} \cos{\left(\frac{6 p}{5} \right)}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} - \frac{169050294000.0 p^{4}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} + \frac{24010000000.0 p^{4} e^{\frac{147}{100}}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} + \frac{16807000000.0 p^{3} e^{\frac{63}{100}} \sin{\left(\frac{6 p}{5} \right)}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} + \frac{38218714632.0 p^{3} \sin{\left(\frac{6 p}{5} \right)}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} - \frac{11764900000.0 p^{2} e^{\frac{63}{100}} \cos{\left(\frac{6 p}{5} \right)}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} + \frac{165669288120.0 p^{2} \cos{\left(\frac{6 p}{5} \right)}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} - \frac{165669288120.0 p^{2}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} + \frac{11764900000.0 p^{2} e^{\frac{147}{100}}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} + \frac{9363585084.84 p \sin{\left(\frac{6 p}{5} \right)}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} + \frac{40588975589.4 \cos{\left(\frac{6 p}{5} \right)}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} - \frac{40588975589.4}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} & \text{otherwise} \end{cases}$$
=
=
/ 147 63 | --- --- | 100 100 | -2.184192 + 1.42857142857143*e - 1.42857142857143*e for p = 0 | | 63 63 63 63 < 147 147 --- --- --- --- | /6*p\ --- --- 4 /6*p\ 2 /6*p\ /6*p\ 3 /6*p\ 5 /6*p\ 5 100 /6*p\ 3 100 /6*p\ 4 /6*p\ 100 2 /6*p\ 100 | 40588975589.4*cos|---| 4 2 4 100 2 100 169050294000.0*p *cos|---| 165669288120.0*p *cos|---| 9363585084.84*p*sin|---| 38218714632.0*p *sin|---| 38998688400.0*p *sin|---| 34300000000.0*p *e *sin|---| 16807000000.0*p *e *sin|---| 24010000000.0*p *cos|---|*e 11764900000.0*p *cos|---|*e | 40588975589.4 \ 5 / 169050294000.0*p 165669288120.0*p 24010000000.0*p *e 11764900000.0*p *e \ 5 / \ 5 / \ 5 / \ 5 / \ 5 / \ 5 / \ 5 / \ 5 / \ 5 / |- ----------------------------------------------------- + ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- + ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- otherwise | 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 6 4 2 \ 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p 34300000000.0*p + 33614000000.0*p + 8235430000.0*p
$$\begin{cases} - 1.42857142857143 e^{\frac{63}{100}} - 2.184192 + 1.42857142857143 e^{\frac{147}{100}} & \text{for}\: p = 0 \\\frac{38998688400.0 p^{5} \sin{\left(\frac{6 p}{5} \right)}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} + \frac{34300000000.0 p^{5} e^{\frac{63}{100}} \sin{\left(\frac{6 p}{5} \right)}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} - \frac{24010000000.0 p^{4} e^{\frac{63}{100}} \cos{\left(\frac{6 p}{5} \right)}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} + \frac{169050294000.0 p^{4} \cos{\left(\frac{6 p}{5} \right)}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} - \frac{169050294000.0 p^{4}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} + \frac{24010000000.0 p^{4} e^{\frac{147}{100}}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} + \frac{16807000000.0 p^{3} e^{\frac{63}{100}} \sin{\left(\frac{6 p}{5} \right)}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} + \frac{38218714632.0 p^{3} \sin{\left(\frac{6 p}{5} \right)}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} - \frac{11764900000.0 p^{2} e^{\frac{63}{100}} \cos{\left(\frac{6 p}{5} \right)}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} + \frac{165669288120.0 p^{2} \cos{\left(\frac{6 p}{5} \right)}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} - \frac{165669288120.0 p^{2}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} + \frac{11764900000.0 p^{2} e^{\frac{147}{100}}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} + \frac{9363585084.84 p \sin{\left(\frac{6 p}{5} \right)}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} + \frac{40588975589.4 \cos{\left(\frac{6 p}{5} \right)}}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} - \frac{40588975589.4}{34300000000.0 p^{6} + 33614000000.0 p^{4} + 8235430000.0 p^{2}} & \text{otherwise} \end{cases}$$
Piecewise((-2.184192 + 1.42857142857143*exp(147/100) - 1.42857142857143*exp(63/100), p = 0), (-40588975589.4/(34300000000.0*p^6 + 33614000000.0*p^4 + 8235430000.0*p^2) + 40588975589.4*cos(6*p/5)/(34300000000.0*p^6 + 33614000000.0*p^4 + 8235430000.0*p^2) - 169050294000.0*p^4/(34300000000.0*p^6 + 33614000000.0*p^4 + 8235430000.0*p^2) - 165669288120.0*p^2/(34300000000.0*p^6 + 33614000000.0*p^4 + 8235430000.0*p^2) + 24010000000.0*p^4*exp(147/100)/(34300000000.0*p^6 + 33614000000.0*p^4 + 8235430000.0*p^2) + 11764900000.0*p^2*exp(147/100)/(34300000000.0*p^6 + 33614000000.0*p^4 + 8235430000.0*p^2) + 169050294000.0*p^4*cos(6*p/5)/(34300000000.0*p^6 + 33614000000.0*p^4 + 8235430000.0*p^2) + 165669288120.0*p^2*cos(6*p/5)/(34300000000.0*p^6 + 33614000000.0*p^4 + 8235430000.0*p^2) + 9363585084.84*p*sin(6*p/5)/(34300000000.0*p^6 + 33614000000.0*p^4 + 8235430000.0*p^2) + 38218714632.0*p^3*sin(6*p/5)/(34300000000.0*p^6 + 33614000000.0*p^4 + 8235430000.0*p^2) + 38998688400.0*p^5*sin(6*p/5)/(34300000000.0*p^6 + 33614000000.0*p^4 + 8235430000.0*p^2) + 34300000000.0*p^5*exp(63/100)*sin(6*p/5)/(34300000000.0*p^6 + 33614000000.0*p^4 + 8235430000.0*p^2) + 16807000000.0*p^3*exp(63/100)*sin(6*p/5)/(34300000000.0*p^6 + 33614000000.0*p^4 + 8235430000.0*p^2) - 24010000000.0*p^4*cos(6*p/5)*exp(63/100)/(34300000000.0*p^6 + 33614000000.0*p^4 + 8235430000.0*p^2) - 11764900000.0*p^2*cos(6*p/5)*exp(63/100)/(34300000000.0*p^6 + 33614000000.0*p^4 + 8235430000.0*p^2), True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.