Sr Examen
Integral de cox^4(5*x) dx
Solución
Ha introducido
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1 / | | 4 | cos (x)*5*x dx | / 0
$$\int\limits_{0}^{1} 5 x \cos^{4}{\left(x \right)}\, dx$$
Integral(cos(x)^4*(5*x), (x, 0, 1))
Respuesta (Indefinida)
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/ | 4 4 2 4 2 4 3 2 2 2 3 | 4 15*sin (x) 25*cos (x) 15*x *cos (x) 15*x *sin (x) 15*x*sin (x)*cos(x) 15*x *cos (x)*sin (x) 25*x*cos (x)*sin(x) | cos (x)*5*x dx = C - ---------- + ---------- + ------------- + ------------- + ------------------- + --------------------- + ------------------- | 32 32 16 16 8 8 8 /
$$\int 5 x \cos^{4}{\left(x \right)}\, dx = C + \frac{15 x^{2} \sin^{4}{\left(x \right)}}{16} + \frac{15 x^{2} \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{8} + \frac{15 x^{2} \cos^{4}{\left(x \right)}}{16} + \frac{15 x \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{8} + \frac{25 x \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{8} - \frac{15 \sin^{4}{\left(x \right)}}{32} + \frac{25 \cos^{4}{\left(x \right)}}{32}$$
Gráfica
Respuesta
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4 4 2 2 3 3 25 15*sin (1) 55*cos (1) 15*cos (1)*sin (1) 15*sin (1)*cos(1) 25*cos (1)*sin(1) - -- + ---------- + ---------- + ------------------ + ----------------- + ----------------- 32 32 32 8 8 8
$$- \frac{25}{32} + \frac{55 \cos^{4}{\left(1 \right)}}{32} + \frac{15 \sin^{4}{\left(1 \right)}}{32} + \frac{15 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{8} + \frac{25 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{8} + \frac{15 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{8}$$
=
=
4 4 2 2 3 3 25 15*sin (1) 55*cos (1) 15*cos (1)*sin (1) 15*sin (1)*cos(1) 25*cos (1)*sin(1) - -- + ---------- + ---------- + ------------------ + ----------------- + ----------------- 32 32 32 8 8 8
$$- \frac{25}{32} + \frac{55 \cos^{4}{\left(1 \right)}}{32} + \frac{15 \sin^{4}{\left(1 \right)}}{32} + \frac{15 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{8} + \frac{25 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{8} + \frac{15 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{8}$$
-25/32 + 15*sin(1)^4/32 + 55*cos(1)^4/32 + 15*cos(1)^2*sin(1)^2/8 + 15*sin(1)^3*cos(1)/8 + 25*cos(1)^3*sin(1)/8
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.