Sr Examen
Integral de (cos^6)(4x) dx
Solución
Ha introducido
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1 / | | 6 | cos (x)*4*x dx | / 0
$$\int\limits_{0}^{1} 4 x \cos^{6}{\left(x \right)}\, dx$$
Integral(cos(x)^6*(4*x), (x, 0, 1))
Respuesta (Indefinida)
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/ | 6 6 4 2 2 6 2 6 5 3 3 5 2 2 4 2 4 2 | 6 5*sin (x) 53*cos (x) 5*cos (x)*sin (x) 5*x *cos (x) 5*x *sin (x) 5*x*sin (x)*cos(x) 10*x*cos (x)*sin (x) 11*x*cos (x)*sin(x) 15*x *cos (x)*sin (x) 15*x *cos (x)*sin (x) | cos (x)*4*x dx = C - --------- + ---------- + ----------------- + ------------ + ------------ + ------------------ + -------------------- + ------------------- + --------------------- + --------------------- | 24 72 6 8 8 4 3 4 8 8 /
$$\int 4 x \cos^{6}{\left(x \right)}\, dx = C + \frac{5 x^{2} \sin^{6}{\left(x \right)}}{8} + \frac{15 x^{2} \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}{8} + \frac{15 x^{2} \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}}{8} + \frac{5 x^{2} \cos^{6}{\left(x \right)}}{8} + \frac{5 x \sin^{5}{\left(x \right)} \cos{\left(x \right)}}{4} + \frac{10 x \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)}}{3} + \frac{11 x \sin{\left(x \right)} \cos^{5}{\left(x \right)}}{4} - \frac{5 \sin^{6}{\left(x \right)}}{24} + \frac{5 \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}}{6} + \frac{53 \cos^{6}{\left(x \right)}}{72}$$
Gráfica
Respuesta
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6 6 5 3 3 5 2 4 4 2 53 5*sin (1) 49*cos (1) 5*sin (1)*cos(1) 10*cos (1)*sin (1) 11*cos (1)*sin(1) 15*cos (1)*sin (1) 65*cos (1)*sin (1) - -- + --------- + ---------- + ---------------- + ------------------ + ----------------- + ------------------ + ------------------ 72 12 36 4 3 4 8 24
$$- \frac{53}{72} + \frac{49 \cos^{6}{\left(1 \right)}}{36} + \frac{11 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{4} + \frac{5 \sin^{6}{\left(1 \right)}}{12} + \frac{65 \sin^{2}{\left(1 \right)} \cos^{4}{\left(1 \right)}}{24} + \frac{15 \sin^{4}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{8} + \frac{5 \sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{4} + \frac{10 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{3}$$
=
=
6 6 5 3 3 5 2 4 4 2 53 5*sin (1) 49*cos (1) 5*sin (1)*cos(1) 10*cos (1)*sin (1) 11*cos (1)*sin(1) 15*cos (1)*sin (1) 65*cos (1)*sin (1) - -- + --------- + ---------- + ---------------- + ------------------ + ----------------- + ------------------ + ------------------ 72 12 36 4 3 4 8 24
$$- \frac{53}{72} + \frac{49 \cos^{6}{\left(1 \right)}}{36} + \frac{11 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{4} + \frac{5 \sin^{6}{\left(1 \right)}}{12} + \frac{65 \sin^{2}{\left(1 \right)} \cos^{4}{\left(1 \right)}}{24} + \frac{15 \sin^{4}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{8} + \frac{5 \sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{4} + \frac{10 \sin^{3}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{3}$$
-53/72 + 5*sin(1)^6/12 + 49*cos(1)^6/36 + 5*sin(1)^5*cos(1)/4 + 10*cos(1)^3*sin(1)^3/3 + 11*cos(1)^5*sin(1)/4 + 15*cos(1)^2*sin(1)^4/8 + 65*cos(1)^4*sin(1)^2/24
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.