Sr Examen
Integral de x*sin^(8)x dx
Solución
Ha introducido
[src]
1 / | | 8 | x*sin (x) dx | / -1
$$\int\limits_{-1}^{1} x \sin^{8}{\left(x \right)}\, dx$$
Integral(x*sin(x)^8, (x, -1, 1))
Respuesta (Indefinida)
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/ | 8 8 4 4 6 2 2 8 2 8 3 5 5 3 7 7 2 2 6 2 6 2 2 4 4 | 8 1211*cos (x) 93*sin (x) 511*cos (x)*sin (x) 7*cos (x)*sin (x) 35*x *cos (x) 35*x *sin (x) 511*x*cos (x)*sin (x) 385*x*cos (x)*sin (x) 93*x*sin (x)*cos(x) 35*x*cos (x)*sin(x) 35*x *cos (x)*sin (x) 35*x *cos (x)*sin (x) 105*x *cos (x)*sin (x) | x*sin (x) dx = C - ------------ + ---------- - ------------------- - ----------------- + ------------- + ------------- - --------------------- - --------------------- - ------------------- - ------------------- + --------------------- + --------------------- + ---------------------- | 9216 1024 1536 18 256 256 384 384 128 128 64 64 128 /
$$\int x \sin^{8}{\left(x \right)}\, dx = C + \frac{35 x^{2} \sin^{8}{\left(x \right)}}{256} + \frac{35 x^{2} \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)}}{64} + \frac{105 x^{2} \sin^{4}{\left(x \right)} \cos^{4}{\left(x \right)}}{128} + \frac{35 x^{2} \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}}{64} + \frac{35 x^{2} \cos^{8}{\left(x \right)}}{256} - \frac{93 x \sin^{7}{\left(x \right)} \cos{\left(x \right)}}{128} - \frac{511 x \sin^{5}{\left(x \right)} \cos^{3}{\left(x \right)}}{384} - \frac{385 x \sin^{3}{\left(x \right)} \cos^{5}{\left(x \right)}}{384} - \frac{35 x \sin{\left(x \right)} \cos^{7}{\left(x \right)}}{128} + \frac{93 \sin^{8}{\left(x \right)}}{1024} - \frac{511 \sin^{4}{\left(x \right)} \cos^{4}{\left(x \right)}}{1536} - \frac{7 \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}}{18} - \frac{1211 \cos^{8}{\left(x \right)}}{9216}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.