Sr Examen
Integral de xdx/(cos^2*(5x)) dx
Solución
Ha introducido
[src]
1 / | | x | --------- dx | 2 | cos (5*x) | / 0
$$\int\limits_{0}^{1} \frac{x}{\cos^{2}{\left(5 x \right)}}\, dx$$
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 / /
$$\int \frac{x}{\cos^{2}{\left(5 x \right)}}\, dx = C - \frac{10 x \tan{\left(\frac{5 x}{2} \right)}}{25 \tan^{2}{\left(\frac{5 x}{2} \right)} - 25} + \frac{\log{\left(\tan{\left(\frac{5 x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{5 x}{2} \right)}}{25 \tan^{2}{\left(\frac{5 x}{2} \right)} - 25} - \frac{\log{\left(\tan{\left(\frac{5 x}{2} \right)} - 1 \right)}}{25 \tan^{2}{\left(\frac{5 x}{2} \right)} - 25} + \frac{\log{\left(\tan{\left(\frac{5 x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{5 x}{2} \right)}}{25 \tan^{2}{\left(\frac{5 x}{2} \right)} - 25} - \frac{\log{\left(\tan{\left(\frac{5 x}{2} \right)} + 1 \right)}}{25 \tan^{2}{\left(\frac{5 x}{2} \right)} - 25} - \frac{\log{\left(\tan^{2}{\left(\frac{5 x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{5 x}{2} \right)}}{25 \tan^{2}{\left(\frac{5 x}{2} \right)} - 25} + \frac{\log{\left(\tan^{2}{\left(\frac{5 x}{2} \right)} + 1 \right)}}{25 \tan^{2}{\left(\frac{5 x}{2} \right)} - 25}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.