Sr Examen
Integral de x^2*sin×3x^3×dx dx
Solución
Ha introducido
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1 / | | 2 3 | x *sin (3*x) dx | / 0
$$\int\limits_{0}^{1} x^{2} \sin^{3}{\left(3 x \right)}\, dx$$
Integral(x^2*sin(3*x)^3, (x, 0, 1))
Respuesta (Indefinida)
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/ | 3 2 3 3 2 2 2 2 | 2 3 40*cos (3*x) 2*x *cos (3*x) 14*x*sin (3*x) 14*sin (3*x)*cos(3*x) x *sin (3*x)*cos(3*x) 4*x*cos (3*x)*sin(3*x) | x *sin (3*x) dx = C + ------------ - -------------- + -------------- + --------------------- - --------------------- + ---------------------- | 729 9 81 243 3 27 /
$$\int x^{2} \sin^{3}{\left(3 x \right)}\, dx = C - \frac{x^{2} \sin^{2}{\left(3 x \right)} \cos{\left(3 x \right)}}{3} - \frac{2 x^{2} \cos^{3}{\left(3 x \right)}}{9} + \frac{14 x \sin^{3}{\left(3 x \right)}}{81} + \frac{4 x \sin{\left(3 x \right)} \cos^{2}{\left(3 x \right)}}{27} + \frac{14 \sin^{2}{\left(3 x \right)} \cos{\left(3 x \right)}}{243} + \frac{40 \cos^{3}{\left(3 x \right)}}{729}$$
Gráfica
Respuesta
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3 3 2 2 40 122*cos (3) 14*sin (3) 67*sin (3)*cos(3) 4*cos (3)*sin(3) - --- - ----------- + ---------- - ----------------- + ---------------- 729 729 81 243 27
$$- \frac{40}{729} + \frac{14 \sin^{3}{\left(3 \right)}}{81} - \frac{67 \sin^{2}{\left(3 \right)} \cos{\left(3 \right)}}{243} + \frac{4 \sin{\left(3 \right)} \cos^{2}{\left(3 \right)}}{27} - \frac{122 \cos^{3}{\left(3 \right)}}{729}$$
=
=
3 3 2 2 40 122*cos (3) 14*sin (3) 67*sin (3)*cos(3) 4*cos (3)*sin(3) - --- - ----------- + ---------- - ----------------- + ---------------- 729 729 81 243 27
$$- \frac{40}{729} + \frac{14 \sin^{3}{\left(3 \right)}}{81} - \frac{67 \sin^{2}{\left(3 \right)} \cos{\left(3 \right)}}{243} + \frac{4 \sin{\left(3 \right)} \cos^{2}{\left(3 \right)}}{27} - \frac{122 \cos^{3}{\left(3 \right)}}{729}$$
-40/729 - 122*cos(3)^3/729 + 14*sin(3)^3/81 - 67*sin(3)^2*cos(3)/243 + 4*cos(3)^2*sin(3)/27
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.