Sr Examen
Integral de x^2cosx^5 dx
Solución
Ha introducido
[src]
1 / | | 2 5 | x *cos (x) dx | / 0
$$\int\limits_{0}^{1} x^{2} \cos^{5}{\left(x \right)}\, dx$$
Integral(x^2*cos(x)^5, (x, 0, 1))
Respuesta (Indefinida)
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/ | 5 2 3 4 2 5 5 2 2 3 4 3 2 | 2 5 4144*sin (x) 1712*cos (x)*sin (x) 298*cos (x)*sin(x) 8*x *sin (x) 298*x*cos (x) 2 4 4*x *cos (x)*sin (x) 16*x*sin (x)*cos(x) 104*x*cos (x)*sin (x) | x *cos (x) dx = C - ------------ - -------------------- - ------------------ + ------------ + ------------- + x *cos (x)*sin(x) + -------------------- + ------------------- + --------------------- | 3375 675 225 15 225 3 15 45 /
$$\int x^{2} \cos^{5}{\left(x \right)}\, dx = C + \frac{8 x^{2} \sin^{5}{\left(x \right)}}{15} + \frac{4 x^{2} \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)}}{3} + x^{2} \sin{\left(x \right)} \cos^{4}{\left(x \right)} + \frac{16 x \sin^{4}{\left(x \right)} \cos{\left(x \right)}}{15} + \frac{104 x \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}{45} + \frac{298 x \cos^{5}{\left(x \right)}}{225} - \frac{4144 \sin^{5}{\left(x \right)}}{3375} - \frac{1712 \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)}}{675} - \frac{298 \sin{\left(x \right)} \cos^{4}{\left(x \right)}}{225}$$
Gráfica
Respuesta
[src]
5 5 2 3 4 4 3 2
2344*sin (1) 298*cos (1) 812*cos (1)*sin (1) 73*cos (1)*sin(1) 16*sin (1)*cos(1) 104*cos (1)*sin (1)
- ------------ + ----------- - ------------------- - ----------------- + ----------------- + -------------------
3375 225 675 225 15 45
$$- \frac{2344 \sin^{5}{\left(1 \right)}}{3375} - \frac{812 \sin^{3}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{675} - \frac{73 \sin{\left(1 \right)} \cos^{4}{\left(1 \right)}}{225} + \frac{298 \cos^{5}{\left(1 \right)}}{225} + \frac{104 \sin^{2}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{45} + \frac{16 \sin^{4}{\left(1 \right)} \cos{\left(1 \right)}}{15}$$
=
=
5 5 2 3 4 4 3 2
2344*sin (1) 298*cos (1) 812*cos (1)*sin (1) 73*cos (1)*sin(1) 16*sin (1)*cos(1) 104*cos (1)*sin (1)
- ------------ + ----------- - ------------------- - ----------------- + ----------------- + -------------------
3375 225 675 225 15 45
$$- \frac{2344 \sin^{5}{\left(1 \right)}}{3375} - \frac{812 \sin^{3}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{675} - \frac{73 \sin{\left(1 \right)} \cos^{4}{\left(1 \right)}}{225} + \frac{298 \cos^{5}{\left(1 \right)}}{225} + \frac{104 \sin^{2}{\left(1 \right)} \cos^{3}{\left(1 \right)}}{45} + \frac{16 \sin^{4}{\left(1 \right)} \cos{\left(1 \right)}}{15}$$
-2344*sin(1)^5/3375 + 298*cos(1)^5/225 - 812*cos(1)^2*sin(1)^3/675 - 73*cos(1)^4*sin(1)/225 + 16*sin(1)^4*cos(1)/15 + 104*cos(1)^3*sin(1)^2/45
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.