Sr Examen
Integral de x^3sin3x^4 dx
Solución
Ha introducido
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1 / | | 3 4 | x *sin (3*x) dx | / 0
$$\int\limits_{0}^{1} x^{3} \sin^{4}{\left(3 x \right)}\, dx$$
Integral(x^3*sin(3*x)^4, (x, 0, 1))
Respuesta (Indefinida)
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/ | 4 4 2 4 4 4 4 4 2 4 3 3 3 3 2 2 2 4 2 2 3 3 | 3 4 17*sin (3*x) 5*cos (3*x) 5*x *cos (3*x) 3*x *cos (3*x) 3*x *sin (3*x) 17*x *sin (3*x) 5*x *sin (3*x)*cos(3*x) x *cos (3*x)*sin(3*x) x *cos (3*x)*sin (3*x) 3*x *cos (3*x)*sin (3*x) 5*x*cos (3*x)*sin(3*x) 17*x*sin (3*x)*cos(3*x) | x *sin (3*x) dx = C - ------------ + ----------- - -------------- + -------------- + -------------- + --------------- - ----------------------- - --------------------- - ---------------------- + ------------------------ + ---------------------- + ----------------------- | 6912 2304 128 32 32 384 24 8 64 16 192 576 /
$$\int x^{3} \sin^{4}{\left(3 x \right)}\, dx = C + \frac{3 x^{4} \sin^{4}{\left(3 x \right)}}{32} + \frac{3 x^{4} \sin^{2}{\left(3 x \right)} \cos^{2}{\left(3 x \right)}}{16} + \frac{3 x^{4} \cos^{4}{\left(3 x \right)}}{32} - \frac{5 x^{3} \sin^{3}{\left(3 x \right)} \cos{\left(3 x \right)}}{24} - \frac{x^{3} \sin{\left(3 x \right)} \cos^{3}{\left(3 x \right)}}{8} + \frac{17 x^{2} \sin^{4}{\left(3 x \right)}}{384} - \frac{x^{2} \sin^{2}{\left(3 x \right)} \cos^{2}{\left(3 x \right)}}{64} - \frac{5 x^{2} \cos^{4}{\left(3 x \right)}}{128} + \frac{17 x \sin^{3}{\left(3 x \right)} \cos{\left(3 x \right)}}{576} + \frac{5 x \sin{\left(3 x \right)} \cos^{3}{\left(3 x \right)}}{192} - \frac{17 \sin^{4}{\left(3 x \right)}}{6912} + \frac{5 \cos^{4}{\left(3 x \right)}}{2304}$$
Gráfica
Respuesta
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4 4 3 3 2 2 5 131*cos (3) 937*sin (3) 103*sin (3)*cos(3) 19*cos (3)*sin(3) 11*cos (3)*sin (3) - ---- + ----------- + ----------- - ------------------ - ----------------- + ------------------ 2304 2304 6912 576 192 64
$$- \frac{5}{2304} + \frac{937 \sin^{4}{\left(3 \right)}}{6912} - \frac{103 \sin^{3}{\left(3 \right)} \cos{\left(3 \right)}}{576} + \frac{11 \sin^{2}{\left(3 \right)} \cos^{2}{\left(3 \right)}}{64} - \frac{19 \sin{\left(3 \right)} \cos^{3}{\left(3 \right)}}{192} + \frac{131 \cos^{4}{\left(3 \right)}}{2304}$$
=
=
4 4 3 3 2 2 5 131*cos (3) 937*sin (3) 103*sin (3)*cos(3) 19*cos (3)*sin(3) 11*cos (3)*sin (3) - ---- + ----------- + ----------- - ------------------ - ----------------- + ------------------ 2304 2304 6912 576 192 64
$$- \frac{5}{2304} + \frac{937 \sin^{4}{\left(3 \right)}}{6912} - \frac{103 \sin^{3}{\left(3 \right)} \cos{\left(3 \right)}}{576} + \frac{11 \sin^{2}{\left(3 \right)} \cos^{2}{\left(3 \right)}}{64} - \frac{19 \sin{\left(3 \right)} \cos^{3}{\left(3 \right)}}{192} + \frac{131 \cos^{4}{\left(3 \right)}}{2304}$$
-5/2304 + 131*cos(3)^4/2304 + 937*sin(3)^4/6912 - 103*sin(3)^3*cos(3)/576 - 19*cos(3)^3*sin(3)/192 + 11*cos(3)^2*sin(3)^2/64
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.