Sr Examen
Integral de (2x^9)cos(4x) dx
Solución
Ha introducido
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pi -- 4 / | | 9 | 2*x *cos(4*x) dx | / -pi ---- 4
$$\int\limits_{- \frac{\pi}{4}}^{\frac{\pi}{4}} 2 x^{9} \cos{\left(4 x \right)}\, dx$$
Integral((2*x^9)*cos(4*x), (x, -pi/4, pi/4))
Respuesta (Indefinida)
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/ | 9 2 3 6 7 8 5 4 | 9 2835*cos(4*x) x *sin(4*x) 2835*x *cos(4*x) 945*x *sin(4*x) 63*x *cos(4*x) 9*x *sin(4*x) 9*x *cos(4*x) 189*x *sin(4*x) 945*x *cos(4*x) 2835*x*sin(4*x) | 2*x *cos(4*x) dx = C + ------------- + ----------- - ---------------- - --------------- - -------------- - ------------- + ------------- + --------------- + --------------- + --------------- | 4096 2 512 128 16 4 8 32 128 1024 /
$$\int 2 x^{9} \cos{\left(4 x \right)}\, dx = C + \frac{x^{9} \sin{\left(4 x \right)}}{2} + \frac{9 x^{8} \cos{\left(4 x \right)}}{8} - \frac{9 x^{7} \sin{\left(4 x \right)}}{4} - \frac{63 x^{6} \cos{\left(4 x \right)}}{16} + \frac{189 x^{5} \sin{\left(4 x \right)}}{32} + \frac{945 x^{4} \cos{\left(4 x \right)}}{128} - \frac{945 x^{3} \sin{\left(4 x \right)}}{128} - \frac{2835 x^{2} \cos{\left(4 x \right)}}{512} + \frac{2835 x \sin{\left(4 x \right)}}{1024} + \frac{2835 \cos{\left(4 x \right)}}{4096}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.