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Resolución de integrales/ cos^2/ xdx/(cos^2*(5x))

Integral de xdx/(cos^2*(5x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1             
  /             
 |              
 |      x       
 |  --------- dx
 |     2        
 |  cos (5*x)   
 |              
/               
0
∫01xcos⁡2(5x) dx\int\limits_{0}^{1} \frac{x}{\cos^{2}{\left(5 x \right)}}\, dx 
Integral(x/cos(5*x)^2, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                      /       2/5*x\\      /       /5*x\\       /        /5*x\\      2/5*x\    /       /5*x\\      2/5*x\    /        /5*x\\      2/5*x\    /       2/5*x\\             /5*x\   
 |                    log|1 + tan |---||   log|1 + tan|---||    log|-1 + tan|---||   tan |---|*log|1 + tan|---||   tan |---|*log|-1 + tan|---||   tan |---|*log|1 + tan |---||     10*x*tan|---|   
 |     x                 \        \ 2 //      \       \ 2 //       \        \ 2 //       \ 2 /    \       \ 2 //       \ 2 /    \        \ 2 //       \ 2 /    \        \ 2 //             \ 2 /   
 | --------- dx = C + ------------------ - ------------------ - ------------------ + --------------------------- + ---------------------------- - ---------------------------- - ------------------
 |    2                           2/5*x\               2/5*x\               2/5*x\                    2/5*x\                        2/5*x\                         2/5*x\                    2/5*x\
 | cos (5*x)          -25 + 25*tan |---|   -25 + 25*tan |---|   -25 + 25*tan |---|        -25 + 25*tan |---|            -25 + 25*tan |---|             -25 + 25*tan |---|        -25 + 25*tan |---|
 |                                 \ 2 /                \ 2 /                \ 2 /                     \ 2 /                         \ 2 /                          \ 2 /                     \ 2 /
/
∫xcos⁡2(5x) dx=C−10xtan⁡(5x2)25tan⁡2(5x2)−25+log⁡(tan⁡(5x2)−1)tan⁡2(5x2)25tan⁡2(5x2)−25−log⁡(tan⁡(5x2)−1)25tan⁡2(5x2)−25+log⁡(tan⁡(5x2)+1)tan⁡2(5x2)25tan⁡2(5x2)−25−log⁡(tan⁡(5x2)+1)25tan⁡2(5x2)−25−log⁡(tan⁡2(5x2)+1)tan⁡2(5x2)25tan⁡2(5x2)−25+log⁡(tan⁡2(5x2)+1)25tan⁡2(5x2)−25\int \frac{x}{\cos^{2}{\left(5 x \right)}}\, dx = C - \frac{10 x \tan{\left(\frac{5 x}{2} \right)}}{25 \tan^{2}{\left(\frac{5 x}{2} \right)} - 25} + \frac{\log{\left(\tan{\left(\frac{5 x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{5 x}{2} \right)}}{25 \tan^{2}{\left(\frac{5 x}{2} \right)} - 25} - \frac{\log{\left(\tan{\left(\frac{5 x}{2} \right)} - 1 \right)}}{25 \tan^{2}{\left(\frac{5 x}{2} \right)} - 25} + \frac{\log{\left(\tan{\left(\frac{5 x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{5 x}{2} \right)}}{25 \tan^{2}{\left(\frac{5 x}{2} \right)} - 25} - \frac{\log{\left(\tan{\left(\frac{5 x}{2} \right)} + 1 \right)}}{25 \tan^{2}{\left(\frac{5 x}{2} \right)} - 25} - \frac{\log{\left(\tan^{2}{\left(\frac{5 x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{5 x}{2} \right)}}{25 \tan^{2}{\left(\frac{5 x}{2} \right)} - 25} + \frac{\log{\left(\tan^{2}{\left(\frac{5 x}{2} \right)} + 1 \right)}}{25 \tan^{2}{\left(\frac{5 x}{2} \right)} - 25}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90500000-250000
Trazar el gráfico f(x)
Respuesta numérica [src] 
184.154417219522
184.154417219522

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

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