Sr Examen
Integral de 2^(-x)*arctg2^x dx
Solución
Ha introducido
[src]
1 / | | -x x | 2 *atan (2) dx | / 0
$$\int\limits_{0}^{1} 2^{- x} \operatorname{atan}^{x}{\left(2 \right)}\, dx$$
Integral(2^(-x)*atan(2)^x, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | x | -x x atan (2) | 2 *atan (2) dx = C - --------------------------- | x x / 2 *log(2) - 2 *log(atan(2))
$$\int 2^{- x} \operatorname{atan}^{x}{\left(2 \right)}\, dx = C - \frac{\operatorname{atan}^{x}{\left(2 \right)}}{- 2^{x} \log{\left(\operatorname{atan}{\left(2 \right)} \right)} + 2^{x} \log{\left(2 \right)}}$$
Gráfica
Respuesta
[src]
1 atan(2) ---------------------- - -------------------------- -log(atan(2)) + log(2) -2*log(atan(2)) + 2*log(2)
$$- \frac{\operatorname{atan}{\left(2 \right)}}{- 2 \log{\left(\operatorname{atan}{\left(2 \right)} \right)} + 2 \log{\left(2 \right)}} + \frac{1}{- \log{\left(\operatorname{atan}{\left(2 \right)} \right)} + \log{\left(2 \right)}}$$
=
=
1 atan(2) ---------------------- - -------------------------- -log(atan(2)) + log(2) -2*log(atan(2)) + 2*log(2)
$$- \frac{\operatorname{atan}{\left(2 \right)}}{- 2 \log{\left(\operatorname{atan}{\left(2 \right)} \right)} + 2 \log{\left(2 \right)}} + \frac{1}{- \log{\left(\operatorname{atan}{\left(2 \right)} \right)} + \log{\left(2 \right)}}$$
1/(-log(atan(2)) + log(2)) - atan(2)/(-2*log(atan(2)) + 2*log(2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.