Sr Examen
Integral de (sin5*x*cos^2)*5*x dx
Solución
Ha introducido
[src]
1 / | | 2 | sin(5*x)*cos (x)*5*x dx | / 0
$$\int\limits_{0}^{1} x 5 \sin{\left(5 x \right)} \cos^{2}{\left(x \right)}\, dx$$
Integral(((sin(5*x)*cos(x)^2)*5)*x, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | 5 3 7 2 3 7 4 3 2 5 6 4 3 2 5 3 4 5 2 3 2 | 2 104*sin (x) 50*sin (x) 13088*sin (x) 260*cos (x)*sin (x) 128*x*cos (x) 40*cos (x)*sin(x) 25*x*cos (x) 25*cos (x)*sin(x) 40*x*cos (x) 128*cos (x)*sin(x) 1216*cos (x)*sin (x) 6544*cos (x)*sin (x) 80*x*cos (x)*sin (x) 64*x*cos (x)*sin (x) 100*x*cos (x)*sin (x) | sin(5*x)*cos (x)*5*x dx = C - ----------- + ---------- + ------------- - ------------------- - ------------- - ----------------- - ------------ + ----------------- + ------------ + ------------------ + -------------------- + -------------------- - -------------------- - -------------------- + --------------------- | 9 9 2205 9 21 3 3 3 3 21 63 315 3 3 3 /
$$\int x 5 \sin{\left(5 x \right)} \cos^{2}{\left(x \right)}\, dx = C - \frac{80 x \sin^{4}{\left(x \right)} \cos^{3}{\left(x \right)}}{3} - \frac{64 x \sin^{2}{\left(x \right)} \cos^{5}{\left(x \right)}}{3} + \frac{100 x \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}{3} - \frac{128 x \cos^{7}{\left(x \right)}}{21} + \frac{40 x \cos^{5}{\left(x \right)}}{3} - \frac{25 x \cos^{3}{\left(x \right)}}{3} + \frac{13088 \sin^{7}{\left(x \right)}}{2205} + \frac{6544 \sin^{5}{\left(x \right)} \cos^{2}{\left(x \right)}}{315} - \frac{104 \sin^{5}{\left(x \right)}}{9} + \frac{1216 \sin^{3}{\left(x \right)} \cos^{4}{\left(x \right)}}{63} - \frac{260 \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)}}{9} + \frac{50 \sin^{3}{\left(x \right)}}{9} + \frac{128 \sin{\left(x \right)} \cos^{6}{\left(x \right)}}{21} - \frac{40 \sin{\left(x \right)} \cos^{4}{\left(x \right)}}{3} + \frac{25 \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{3}$$
Gráfica
Respuesta
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2 2 2 2
142*sin (1)*sin(5) 23*cos (1)*cos(5) 2*sin (1)*cos(5) 583*cos (1)*sin(5) 100*cos(1)*cos(5)*sin(1) 10*cos(1)*sin(1)*sin(5)
- ------------------ - ----------------- + ---------------- + ------------------ - ------------------------ - -----------------------
2205 21 21 2205 441 21
$$- \frac{23 \cos^{2}{\left(1 \right)} \cos{\left(5 \right)}}{21} + \frac{583 \sin{\left(5 \right)} \cos^{2}{\left(1 \right)}}{2205} - \frac{100 \sin{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(5 \right)}}{441} + \frac{2 \sin^{2}{\left(1 \right)} \cos{\left(5 \right)}}{21} - \frac{142 \sin^{2}{\left(1 \right)} \sin{\left(5 \right)}}{2205} - \frac{10 \sin{\left(1 \right)} \sin{\left(5 \right)} \cos{\left(1 \right)}}{21}$$
=
=
2 2 2 2
142*sin (1)*sin(5) 23*cos (1)*cos(5) 2*sin (1)*cos(5) 583*cos (1)*sin(5) 100*cos(1)*cos(5)*sin(1) 10*cos(1)*sin(1)*sin(5)
- ------------------ - ----------------- + ---------------- + ------------------ - ------------------------ - -----------------------
2205 21 21 2205 441 21
$$- \frac{23 \cos^{2}{\left(1 \right)} \cos{\left(5 \right)}}{21} + \frac{583 \sin{\left(5 \right)} \cos^{2}{\left(1 \right)}}{2205} - \frac{100 \sin{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(5 \right)}}{441} + \frac{2 \sin^{2}{\left(1 \right)} \cos{\left(5 \right)}}{21} - \frac{142 \sin^{2}{\left(1 \right)} \sin{\left(5 \right)}}{2205} - \frac{10 \sin{\left(1 \right)} \sin{\left(5 \right)} \cos{\left(1 \right)}}{21}$$
-142*sin(1)^2*sin(5)/2205 - 23*cos(1)^2*cos(5)/21 + 2*sin(1)^2*cos(5)/21 + 583*cos(1)^2*sin(5)/2205 - 100*cos(1)*cos(5)*sin(1)/441 - 10*cos(1)*sin(1)*sin(5)/21
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.