Sr Examen
Integral de (tanx)^4*secx dx
Solución
Ha introducido
[src]
1 / | | 4 | tan (x)*sec(x) dx | / 0
$$\int\limits_{0}^{1} \tan^{4}{\left(x \right)} \sec{\left(x \right)}\, dx$$
Integral(tan(x)^4*sec(x), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | 3 | 4 3*log(-1 + sin(x)) 3*log(1 + sin(x)) -3*sin(x) + 5*sin (x) | tan (x)*sec(x) dx = C - ------------------ + ----------------- + -------------------------- | 16 16 2 4 / 8 - 16*sin (x) + 8*sin (x)
$$\int \tan^{4}{\left(x \right)} \sec{\left(x \right)}\, dx = C + \frac{5 \sin^{3}{\left(x \right)} - 3 \sin{\left(x \right)}}{8 \sin^{4}{\left(x \right)} - 16 \sin^{2}{\left(x \right)} + 8} - \frac{3 \log{\left(\sin{\left(x \right)} - 1 \right)}}{16} + \frac{3 \log{\left(\sin{\left(x \right)} + 1 \right)}}{16}$$
Gráfica
Respuesta
[src]
3
3*log(1 - sin(1)) 3*log(1 + sin(1)) -3*sin(1) + 5*sin (1)
- ----------------- + ----------------- + --------------------------
16 16 2 4
8 - 16*sin (1) + 8*sin (1)
$$\frac{3 \log{\left(\sin{\left(1 \right)} + 1 \right)}}{16} - \frac{3 \log{\left(1 - \sin{\left(1 \right)} \right)}}{16} + \frac{- 3 \sin{\left(1 \right)} + 5 \sin^{3}{\left(1 \right)}}{- 16 \sin^{2}{\left(1 \right)} + 8 \sin^{4}{\left(1 \right)} + 8}$$
=
=
3
3*log(1 - sin(1)) 3*log(1 + sin(1)) -3*sin(1) + 5*sin (1)
- ----------------- + ----------------- + --------------------------
16 16 2 4
8 - 16*sin (1) + 8*sin (1)
$$\frac{3 \log{\left(\sin{\left(1 \right)} + 1 \right)}}{16} - \frac{3 \log{\left(1 - \sin{\left(1 \right)} \right)}}{16} + \frac{- 3 \sin{\left(1 \right)} + 5 \sin^{3}{\left(1 \right)}}{- 16 \sin^{2}{\left(1 \right)} + 8 \sin^{4}{\left(1 \right)} + 8}$$
-3*log(1 - sin(1))/16 + 3*log(1 + sin(1))/16 + (-3*sin(1) + 5*sin(1)^3)/(8 - 16*sin(1)^2 + 8*sin(1)^4)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.