Sr Examen
Integral de tg2x*sqrt(1+2tg^2(2x)+2) dx
Solución
Ha introducido
[src]
pi -- 6 / | | _____________________ | / 2 | tan(2*x)*\/ 1 + 2*tan (2*x) + 2 dx | / 0
$$\int\limits_{0}^{\frac{\pi}{6}} \sqrt{\left(2 \tan^{2}{\left(2 x \right)} + 1\right) + 2} \tan{\left(2 x \right)}\, dx$$
Integral(tan(2*x)*sqrt(1 + 2*tan(2*x)^2 + 2), (x, 0, pi/6))
Respuesta (Indefinida)
[src]
/ | _________________ / _________________\ / _________________\ | _____________________ / 2 | / 2 | | / 2 | | / 2 \/ 3 + 2*tan (2*x) log\1 + \/ 3 + 2*tan (2*x) / log\-1 + \/ 3 + 2*tan (2*x) / | tan(2*x)*\/ 1 + 2*tan (2*x) + 2 dx = C + -------------------- - ----------------------------- + ------------------------------ | 2 4 4 /
$$\int \sqrt{\left(2 \tan^{2}{\left(2 x \right)} + 1\right) + 2} \tan{\left(2 x \right)}\, dx = C + \frac{\sqrt{2 \tan^{2}{\left(2 x \right)} + 3}}{2} + \frac{\log{\left(\sqrt{2 \tan^{2}{\left(2 x \right)} + 3} - 1 \right)}}{4} - \frac{\log{\left(\sqrt{2 \tan^{2}{\left(2 x \right)} + 3} + 1 \right)}}{4}$$
Gráfica
Respuesta
[src]
___ / ___\ / ___\ 3 \/ 3 log(4) log\-1 + \/ 3 / log(2) log\1 + \/ 3 / - - ----- - ------ - --------------- + ------ + -------------- 2 2 4 4 4 4
$$- \frac{\sqrt{3}}{2} - \frac{\log{\left(4 \right)}}{4} - \frac{\log{\left(-1 + \sqrt{3} \right)}}{4} + \frac{\log{\left(2 \right)}}{4} + \frac{\log{\left(1 + \sqrt{3} \right)}}{4} + \frac{3}{2}$$
=
=
___ / ___\ / ___\ 3 \/ 3 log(4) log\-1 + \/ 3 / log(2) log\1 + \/ 3 / - - ----- - ------ - --------------- + ------ + -------------- 2 2 4 4 4 4
$$- \frac{\sqrt{3}}{2} - \frac{\log{\left(4 \right)}}{4} - \frac{\log{\left(-1 + \sqrt{3} \right)}}{4} + \frac{\log{\left(2 \right)}}{4} + \frac{\log{\left(1 + \sqrt{3} \right)}}{4} + \frac{3}{2}$$
3/2 - sqrt(3)/2 - log(4)/4 - log(-1 + sqrt(3))/4 + log(2)/4 + log(1 + sqrt(3))/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.