Sr Examen
Integral de 1/xcos^2(lnx) dx
Solución
Ha introducido
[src]
1 / | | 2 | cos (log(x)) | ------------ dx | x | / 0
$$\int\limits_{0}^{1} \frac{\cos^{2}{\left(\log{\left(x \right)} \right)}}{x}\, dx$$
Integral(cos(log(x))^2/x, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | 3/log(x)\ /log(x)\ 4/log(x)\ 2/log(x)\ | 2 2*tan |------| 2*tan|------| tan |------|*log(x) 2*tan |------|*log(x) | cos (log(x)) log(x) \ 2 / \ 2 / \ 2 / \ 2 / | ------------ dx = C + ----------------------------------- - ----------------------------------- + ----------------------------------- + ----------------------------------- + ----------------------------------- | x 4/log(x)\ 2/log(x)\ 4/log(x)\ 2/log(x)\ 4/log(x)\ 2/log(x)\ 4/log(x)\ 2/log(x)\ 4/log(x)\ 2/log(x)\ | 2 + 2*tan |------| + 4*tan |------| 2 + 2*tan |------| + 4*tan |------| 2 + 2*tan |------| + 4*tan |------| 2 + 2*tan |------| + 4*tan |------| 2 + 2*tan |------| + 4*tan |------| / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 /
$$\int \frac{\cos^{2}{\left(\log{\left(x \right)} \right)}}{x}\, dx = C + \frac{\log{\left(x \right)} \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)}}{2 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 4 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 2} + \frac{2 \log{\left(x \right)} \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)}}{2 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 4 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 2} + \frac{\log{\left(x \right)}}{2 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 4 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 2} - \frac{2 \tan^{3}{\left(\frac{\log{\left(x \right)}}{2} \right)}}{2 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 4 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 2} + \frac{2 \tan{\left(\frac{\log{\left(x \right)}}{2} \right)}}{2 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 4 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 2}$$
Respuesta
[src]
1 / | | 2 | cos (log(x)) | ------------ dx | x | / 0
$$\int\limits_{0}^{1} \frac{\cos^{2}{\left(\log{\left(x \right)} \right)}}{x}\, dx$$
=
=
1 / | | 2 | cos (log(x)) | ------------ dx | x | / 0
$$\int\limits_{0}^{1} \frac{\cos^{2}{\left(\log{\left(x \right)} \right)}}{x}\, dx$$
Integral(cos(log(x))^2/x, (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.