Integral of sin^2(x)*cos^4(x) dx
The solution
The answer (Indefinite)
[src]
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| 3
| 2 4 sin(4*x) x sin (2*x)
| sin (x)*cos (x) dx = C - -------- + -- + ---------
| 64 16 48
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$$\int \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}\, dx = C + \frac{x}{16} + \frac{\sin^{3}{\left(2 x \right)}}{48} - \frac{\sin{\left(4 x \right)}}{64}$$
5 3
1 cos (1)*sin(1) cos(1)*sin(1) cos (1)*sin(1)
-- - -------------- + ------------- + --------------
16 6 16 24
$$- \frac{\sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{6} + \frac{\sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{24} + \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{16} + \frac{1}{16}$$
=
5 3
1 cos (1)*sin(1) cos(1)*sin(1) cos (1)*sin(1)
-- - -------------- + ------------- + --------------
16 6 16 24
$$- \frac{\sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{6} + \frac{\sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{24} + \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{16} + \frac{1}{16}$$
1/16 - cos(1)^5*sin(1)/6 + cos(1)*sin(1)/16 + cos(1)^3*sin(1)/24
Use the examples entering the upper and lower limits of integration.