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Identical expressions
- (x^2sinxcos2x)
- (x squared sinus of x co sinus of e of 2x)
- (x2sinxcos2x)
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- (x²sinxcos2x)
- (x to the power of 2sinxcos2x)
- x^2sinxcos2x
- (x^2sinxcos2x)dx
Integral of (x^2sinxcos2x) dx
The solution
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pi -- 4 / | | 2 | x *sin(x)*cos(2*x) dx | / -pi ---- 4
$$\int\limits_{- \frac{\pi}{4}}^{\frac{\pi}{4}} x^{2} \sin{\left(x \right)} \cos{\left(2 x \right)}\, dx$$
Integral((x^2*sin(x))*cos(2*x), (x, -pi/4, pi/4))
The answer (Indefinite)
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/ | 3 / 3 \ 3 2 2 | 2 28*cos (x) 2 | 2*cos (x) | 8*x*sin (x) 8*sin (x)*cos(x) 4*x*cos (x)*sin(x) | x *sin(x)*cos(2*x) dx = C - 2*cos(x) + ---------- + x *|- --------- + cos(x)| - 2*x*sin(x) + ----------- + ---------------- + ------------------ | 27 \ 3 / 9 9 3 /
$$\int x^{2} \sin{\left(x \right)} \cos{\left(2 x \right)}\, dx = C + x^{2} \left(- \frac{2 \cos^{3}{\left(x \right)}}{3} + \cos{\left(x \right)}\right) + \frac{8 x \sin^{3}{\left(x \right)}}{9} + \frac{4 x \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{3} - 2 x \sin{\left(x \right)} + \frac{8 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{9} + \frac{28 \cos^{3}{\left(x \right)}}{27} - 2 \cos{\left(x \right)}$$
Use the examples entering the upper and lower limits of integration.