Sr Examen
Integral de cos^6bxdx dx
Solución
Ha introducido
[src]
1 / | | 6 | cos (b*x) dx | / 0
$$\int\limits_{0}^{1} \cos^{6}{\left(b x \right)}\, dx$$
Integral(cos(b*x)^6, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ x for b = 0
|
| / 3 \
| | sin (2*b*x)|
<-|-sin(2*b*x) + -----------| // x for b = 0\ // x for b = 0\
| \ 3 / || | || |
/ |----------------------------- otherwise 3*|
$$\int \cos^{6}{\left(b x \right)}\, dx = C + \frac{5 x}{16} + \frac{\begin{cases} x & \text{for}\: b = 0 \\- \frac{\frac{\sin^{3}{\left(2 b x \right)}}{3} - \sin{\left(2 b x \right)}}{2 b} & \text{otherwise} \end{cases}}{8} + \frac{3 \left(\begin{cases} x & \text{for}\: b = 0 \\\frac{\sin{\left(2 b x \right)}}{2 b} & \text{otherwise} \end{cases}\right)}{8} + \frac{3 \left(\begin{cases} x & \text{for}\: b = 0 \\\frac{\sin{\left(4 b x \right)}}{4 b} & \text{otherwise} \end{cases}\right)}{16}$$
Respuesta
[src]
/ 5 3 |5*b cos (b)*sin(b) 5*cos(b)*sin(b) 5*cos (b)*sin(b) |--- + -------------- + --------------- + ---------------- | 16 6 16 24 <--------------------------------------------------------- for And(b > -oo, b < oo, b != 0) | b | | 1 otherwise \
$$\begin{cases} \frac{\frac{5 b}{16} + \frac{\sin{\left(b \right)} \cos^{5}{\left(b \right)}}{6} + \frac{5 \sin{\left(b \right)} \cos^{3}{\left(b \right)}}{24} + \frac{5 \sin{\left(b \right)} \cos{\left(b \right)}}{16}}{b} & \text{for}\: b > -\infty \wedge b < \infty \wedge b \neq 0 \\1 & \text{otherwise} \end{cases}$$
=
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/ 5 3 |5*b cos (b)*sin(b) 5*cos(b)*sin(b) 5*cos (b)*sin(b) |--- + -------------- + --------------- + ---------------- | 16 6 16 24 <--------------------------------------------------------- for And(b > -oo, b < oo, b != 0) | b | | 1 otherwise \
$$\begin{cases} \frac{\frac{5 b}{16} + \frac{\sin{\left(b \right)} \cos^{5}{\left(b \right)}}{6} + \frac{5 \sin{\left(b \right)} \cos^{3}{\left(b \right)}}{24} + \frac{5 \sin{\left(b \right)} \cos{\left(b \right)}}{16}}{b} & \text{for}\: b > -\infty \wedge b < \infty \wedge b \neq 0 \\1 & \text{otherwise} \end{cases}$$
Piecewise(((5*b/16 + cos(b)^5*sin(b)/6 + 5*cos(b)*sin(b)/16 + 5*cos(b)^3*sin(b)/24)/b, (b > -oo)∧(b < oo)∧(Ne(b, 0))), (1, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.