Sr Examen
Integral de cos^2(loge(x)) dx
Solución
Ha introducido
[src]
1 / | | 2/ log(x)\ | cos |-------| dx | | / 1\| | \log\e // | / 0
$$\int\limits_{0}^{1} \cos^{2}{\left(\frac{\log{\left(x \right)}}{\log{\left(e^{1} \right)}} \right)}\, dx$$
Integral(cos(log(x)/log(exp(1)))^2, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ 3/log(x)\ 2/log(x)\ 4/log(x)\ /log(x)\ | 4*x*tan |------| 2*x*tan |------| 3*x*tan |------| 4*x*tan|------| | 2/ log(x)\ 3*x \ 2 / \ 2 / \ 2 / \ 2 / | cos |-------| dx = C + ------------------------------------ - ------------------------------------ + ------------------------------------ + ------------------------------------ + ------------------------------------ | | / 1\| 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)\ | \log\e // 5 + 5*tan |------| + 10*tan |------| 5 + 5*tan |------| + 10*tan |------| 5 + 5*tan |------| + 10*tan |------| 5 + 5*tan |------| + 10*tan |------| 5 + 5*tan |------| + 10*tan |------| | \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / \ 2 / /
$$\int \cos^{2}{\left(\frac{\log{\left(x \right)}}{\log{\left(e^{1} \right)}} \right)}\, dx = C + \frac{3 x \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)}}{5 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 10 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 5} - \frac{4 x \tan^{3}{\left(\frac{\log{\left(x \right)}}{2} \right)}}{5 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 10 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 5} + \frac{2 x \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)}}{5 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 10 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 5} + \frac{4 x \tan{\left(\frac{\log{\left(x \right)}}{2} \right)}}{5 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 10 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 5} + \frac{3 x}{5 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 10 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 5}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.