Sr Examen
Integral de (12+6x)sin(pinx) dx
Solución
Ha introducido
[src]
1 / | | (12 + 6*x)*sin(p*log(x)) dx | / 0
$$\int\limits_{0}^{1} \left(6 x + 12\right) \sin{\left(p \log{\left(x \right)} \right)}\, dx$$
Integral((12 + 6*x)*sin(p*log(x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
// 4 \ // 2 \
|| I*log(x) I*x | || I*log(x) I*x |
|| -------- - ---- for p = -2*I| || -------- - ---- for p = -I|
|| 2 8 | || 2 4 |
|| | || |
/ || 4 | || 2 |
| || I*log(x) I*x | || I*log(x) I*x |
| (12 + 6*x)*sin(p*log(x)) dx = C + 6*|< - -------- + ---- for p = 2*I | + 12*|< - -------- + ---- for p = I |
| || 2 8 | || 2 4 |
/ || | || |
|| 2 2 | ||x*sin(p*log(x)) p*x*cos(p*log(x)) |
||2*x *sin(p*log(x)) p*x *cos(p*log(x)) | ||--------------- - ----------------- otherwise |
||------------------ - ------------------ otherwise | || 2 2 |
|| 2 2 | || 1 + p 1 + p |
\\ 4 + p 4 + p / \\ /
$$\int \left(6 x + 12\right) \sin{\left(p \log{\left(x \right)} \right)}\, dx = C + 12 \left(\begin{cases} - \frac{i x^{2}}{4} + \frac{i \log{\left(x \right)}}{2} & \text{for}\: p = - i \\\frac{i x^{2}}{4} - \frac{i \log{\left(x \right)}}{2} & \text{for}\: p = i \\- \frac{p x \cos{\left(p \log{\left(x \right)} \right)}}{p^{2} + 1} + \frac{x \sin{\left(p \log{\left(x \right)} \right)}}{p^{2} + 1} & \text{otherwise} \end{cases}\right) + 6 \left(\begin{cases} - \frac{i x^{4}}{8} + \frac{i \log{\left(x \right)}}{2} & \text{for}\: p = - 2 i \\\frac{i x^{4}}{8} - \frac{i \log{\left(x \right)}}{2} & \text{for}\: p = 2 i \\- \frac{p x^{2} \cos{\left(p \log{\left(x \right)} \right)}}{p^{2} + 4} + \frac{2 x^{2} \sin{\left(p \log{\left(x \right)} \right)}}{p^{2} + 4} & \text{otherwise} \end{cases}\right)$$
Respuesta
[src]
3
54*p 18*p
- ------------- - -------------
4 2 4 2
4 + p + 5*p 4 + p + 5*p
$$- \frac{18 p^{3}}{p^{4} + 5 p^{2} + 4} - \frac{54 p}{p^{4} + 5 p^{2} + 4}$$
=
=
3
54*p 18*p
- ------------- - -------------
4 2 4 2
4 + p + 5*p 4 + p + 5*p
$$- \frac{18 p^{3}}{p^{4} + 5 p^{2} + 4} - \frac{54 p}{p^{4} + 5 p^{2} + 4}$$
-54*p/(4 + p^4 + 5*p^2) - 18*p^3/(4 + p^4 + 5*p^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.