Sr Examen
Integral de x^2sinx^6 dx
Solución
Ha introducido
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oo / | | 2 6 | x *sin (x) dx | / 1
$$\int\limits_{1}^{\infty} x^{2} \sin^{6}{\left(x \right)}\, dx$$
Integral(x^2*sin(x)^6, (x, 1, oo))
Respuesta (Indefinida)
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/ | 6 3 6 3 6 3 3 5 6 5 4 2 2 5 2 3 3 2 5 3 2 4 3 4 2 2 4 | 2 6 245*x*cos (x) 5*x *cos (x) 5*x *sin (x) 25*cos (x)*sin (x) 245*cos (x)*sin(x) 299*x*sin (x) 299*sin (x)*cos(x) 125*x*cos (x)*sin (x) 11*x *sin (x)*cos(x) 5*x *cos (x)*sin (x) 5*x *cos (x)*sin(x) 5*x *cos (x)*sin (x) 5*x *cos (x)*sin (x) 35*x*cos (x)*sin (x) | x *sin (x) dx = C - ------------- + ------------ + ------------ + ------------------ + ------------------ + ------------- + ------------------ - --------------------- - -------------------- - -------------------- - ------------------- + -------------------- + -------------------- + -------------------- | 1152 48 48 54 1152 1152 1152 384 16 6 16 16 16 384 /
$$\int x^{2} \sin^{6}{\left(x \right)}\, dx = C + \frac{5 x^{3} \sin^{6}{\left(x \right)}}{48} + \frac{5 x^{3} \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}{16} + \frac{5 x^{3} \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}}{16} + \frac{5 x^{3} \cos^{6}{\left(x \right)}}{48} - \frac{11 x^{2} \sin^{5}{\left(x \right)} \cos{\left(x \right)}}{16} - \frac{5 x^{2} \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)}}{6} - \frac{5 x^{2} \sin{\left(x \right)} \cos^{5}{\left(x \right)}}{16} + \frac{299 x \sin^{6}{\left(x \right)}}{1152} + \frac{35 x \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}{384} - \frac{125 x \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}}{384} - \frac{245 x \cos^{6}{\left(x \right)}}{1152} + \frac{299 \sin^{5}{\left(x \right)} \cos{\left(x \right)}}{1152} + \frac{25 \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)}}{54} + \frac{245 \sin{\left(x \right)} \cos^{5}{\left(x \right)}}{1152}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.