Sr Examen
Integral de sinx(1+2/x^3sinx-4ctgx) dx
Solución
Ha introducido
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1 / | | / 2 \ | sin(x)*|1 + --*sin(x) - 4*cot(x)| dx | | 3 | | \ x / | / 0
$$\int\limits_{0}^{1} \left(\left(\frac{2}{x^{3}} \sin{\left(x \right)} + 1\right) - 4 \cot{\left(x \right)}\right) \sin{\left(x \right)}\, dx$$
Integral(sin(x)*(1 + (2/x^3)*sin(x) - 4*cot(x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | / 2 \ 1 cos(2*x) sin(2*x) / 2\ | sin(x)*|1 + --*sin(x) - 4*cot(x)| dx = C - cos(x) - 4*sin(x) - 2*log(x) + 2*Ci(2*x) - ---- + -------- - -------- + log\x / | | 3 | 2 2 x | \ x / 2*x 2*x | /
$$\int \left(\left(\frac{2}{x^{3}} \sin{\left(x \right)} + 1\right) - 4 \cot{\left(x \right)}\right) \sin{\left(x \right)}\, dx = C - 2 \log{\left(x \right)} + \log{\left(x^{2} \right)} - 4 \sin{\left(x \right)} - \cos{\left(x \right)} + 2 \operatorname{Ci}{\left(2 x \right)} - \frac{\sin{\left(2 x \right)}}{x} + \frac{\cos{\left(2 x \right)}}{2 x^{2}} - \frac{1}{2 x^{2}}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.