Integral of x(sin²(x)) dx
The solution
The answer (Indefinite)
[src]
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| 2 2 2 2 2
| 2 sin (x) x *cos (x) x *sin (x) x*cos(x)*sin(x)
| x*sin (x) dx = C + ------- + ---------- + ---------- - ---------------
| 4 4 4 2
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$$\int x \sin^{2}{\left(x \right)}\, dx = C + \frac{x^{2} \sin^{2}{\left(x \right)}}{4} + \frac{x^{2} \cos^{2}{\left(x \right)}}{4} - \frac{x \sin{\left(x \right)} \cos{\left(x \right)}}{2} + \frac{\sin^{2}{\left(x \right)}}{4}$$
2 2
sin (1) cos (1) cos(1)*sin(1)
------- + ------- - -------------
2 4 2
$$- \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{2} + \frac{\cos^{2}{\left(1 \right)}}{4} + \frac{\sin^{2}{\left(1 \right)}}{2}$$
=
2 2
sin (1) cos (1) cos(1)*sin(1)
------- + ------- - -------------
2 4 2
$$- \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{2} + \frac{\cos^{2}{\left(1 \right)}}{4} + \frac{\sin^{2}{\left(1 \right)}}{2}$$
sin(1)^2/2 + cos(1)^2/4 - cos(1)*sin(1)/2
Use the examples entering the upper and lower limits of integration.