Sr Examen
Integral de sin^2(x)/cos^10(x) dx
Solución
Ha introducido
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1 / | | 2 | sin (x) | -------- dx | 10 | cos (x) | / 0
$$\int\limits_{0}^{1} \frac{\sin^{2}{\left(x \right)}}{\cos^{10}{\left(x \right)}}\, dx$$
Integral(sin(x)^2/cos(x)^10, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | 2 | sin (x) 16*sin(x) 8*sin(x) 2*sin(x) sin(x) sin(x) | -------- dx = C - ---------- - ----------- - ----------- - ---------- + --------- | 10 315*cos(x) 3 5 7 9 | cos (x) 315*cos (x) 105*cos (x) 63*cos (x) 9*cos (x) | /
$$\int \frac{\sin^{2}{\left(x \right)}}{\cos^{10}{\left(x \right)}}\, dx = C - \frac{16 \sin{\left(x \right)}}{315 \cos{\left(x \right)}} - \frac{8 \sin{\left(x \right)}}{315 \cos^{3}{\left(x \right)}} - \frac{2 \sin{\left(x \right)}}{105 \cos^{5}{\left(x \right)}} - \frac{\sin{\left(x \right)}}{63 \cos^{7}{\left(x \right)}} + \frac{\sin{\left(x \right)}}{9 \cos^{9}{\left(x \right)}}$$
Gráfica
Respuesta
[src]
16*sin(1) 8*sin(1) 2*sin(1) sin(1) sin(1)
- ---------- - ----------- - ----------- - ---------- + ---------
315*cos(1) 3 5 7 9
315*cos (1) 105*cos (1) 63*cos (1) 9*cos (1)
$$- \frac{\sin{\left(1 \right)}}{63 \cos^{7}{\left(1 \right)}} - \frac{2 \sin{\left(1 \right)}}{105 \cos^{5}{\left(1 \right)}} - \frac{8 \sin{\left(1 \right)}}{315 \cos^{3}{\left(1 \right)}} - \frac{16 \sin{\left(1 \right)}}{315 \cos{\left(1 \right)}} + \frac{\sin{\left(1 \right)}}{9 \cos^{9}{\left(1 \right)}}$$
=
=
16*sin(1) 8*sin(1) 2*sin(1) sin(1) sin(1)
- ---------- - ----------- - ----------- - ---------- + ---------
315*cos(1) 3 5 7 9
315*cos (1) 105*cos (1) 63*cos (1) 9*cos (1)
$$- \frac{\sin{\left(1 \right)}}{63 \cos^{7}{\left(1 \right)}} - \frac{2 \sin{\left(1 \right)}}{105 \cos^{5}{\left(1 \right)}} - \frac{8 \sin{\left(1 \right)}}{315 \cos^{3}{\left(1 \right)}} - \frac{16 \sin{\left(1 \right)}}{315 \cos{\left(1 \right)}} + \frac{\sin{\left(1 \right)}}{9 \cos^{9}{\left(1 \right)}}$$
-16*sin(1)/(315*cos(1)) - 8*sin(1)/(315*cos(1)^3) - 2*sin(1)/(105*cos(1)^5) - sin(1)/(63*cos(1)^7) + sin(1)/(9*cos(1)^9)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.