Sr Examen
Integral de (sin^2)x(cos^3)xdx dx
Solución
Ha introducido
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1 / | | 2 3 | sin (x)*x*cos (x)*x dx | / 0
$$\int\limits_{0}^{1} x x \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}\, dx$$
Integral(((sin(x)^2*x)*cos(x)^3)*x, (x, 0, 1))
Respuesta (Indefinida)
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/ | 5 2 3 4 2 5 5 2 2 3 4 3 2 | 2 3 856*sin (x) 338*cos (x)*sin (x) 52*cos (x)*sin(x) 2*x *sin (x) 52*x*cos (x) x *cos (x)*sin (x) 4*x*sin (x)*cos(x) 26*x*cos (x)*sin (x) | sin (x)*x*cos (x)*x dx = C - ----------- - ------------------- - ----------------- + ------------ + ------------ + ------------------ + ------------------ + -------------------- | 3375 675 225 15 225 3 15 45 /
$$\int x x \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}\, dx = C + \frac{2 x^{2} \sin^{5}{\left(x \right)}}{15} + \frac{x^{2} \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)}}{3} + \frac{4 x \sin^{4}{\left(x \right)} \cos{\left(x \right)}}{15} + \frac{26 x \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}{45} + \frac{52 x \cos^{5}{\left(x \right)}}{225} - \frac{856 \sin^{5}{\left(x \right)}}{3375} - \frac{338 \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)}}{675} - \frac{52 \sin{\left(x \right)} \cos^{4}{\left(x \right)}}{225}$$
Gráfica
Respuesta
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5 5 2 3 4 4 3 2
406*sin (1) 52*cos (1) 113*cos (1)*sin (1) 52*cos (1)*sin(1) 4*sin (1)*cos(1) 26*cos (1)*sin (1)
- ----------- + ---------- - ------------------- - ----------------- + ---------------- + ------------------
3375 225 675 225 15 45
$$- \frac{406 \sin^{5}{\left(1 \right)}}{3375} - \frac{113 \sin^{3}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{675} - \frac{52 \sin{\left(1 \right)} \cos^{4}{\left(1 \right)}}{225} + \frac{52 \cos^{5}{\left(1 \right)}}{225} + \frac{26 \sin^{2}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{45} + \frac{4 \sin^{4}{\left(1 \right)} \cos{\left(1 \right)}}{15}$$
=
=
5 5 2 3 4 4 3 2
406*sin (1) 52*cos (1) 113*cos (1)*sin (1) 52*cos (1)*sin(1) 4*sin (1)*cos(1) 26*cos (1)*sin (1)
- ----------- + ---------- - ------------------- - ----------------- + ---------------- + ------------------
3375 225 675 225 15 45
$$- \frac{406 \sin^{5}{\left(1 \right)}}{3375} - \frac{113 \sin^{3}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{675} - \frac{52 \sin{\left(1 \right)} \cos^{4}{\left(1 \right)}}{225} + \frac{52 \cos^{5}{\left(1 \right)}}{225} + \frac{26 \sin^{2}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{45} + \frac{4 \sin^{4}{\left(1 \right)} \cos{\left(1 \right)}}{15}$$
-406*sin(1)^5/3375 + 52*cos(1)^5/225 - 113*cos(1)^2*sin(1)^3/675 - 52*cos(1)^4*sin(1)/225 + 4*sin(1)^4*cos(1)/15 + 26*cos(1)^3*sin(1)^2/45
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.