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cos(x)^6
Solving integrals/ cos(x)^6

Integral of cos(x)^6 dx

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The solution

You have entered [src] 
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∫01cos⁡6(x) dx\int\limits_{0}^{1} \cos^{6}{\left(x \right)}\, dx 
Integral(cos(x)^6, (x, 0, 1))
The graph
0.001.000.100.200.300.400.500.600.700.800.9002
Plot the graph f(x)
The answer [src] 
        5                                    3          
5    cos (1)*sin(1)   5*cos(1)*sin(1)   5*cos (1)*sin(1)
-- + -------------- + --------------- + ----------------
16         6                 16                24
sin⁡(1)cos⁡5(1)6+5sin⁡(1)cos⁡3(1)24+5sin⁡(1)cos⁡(1)16+516\frac{\sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{6} + \frac{5 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{24} + \frac{5 \sin{\left(1 \right)} \cos{\left(1 \right)}}{16} + \frac{5}{16} 
=
= 
        5                                    3          
5    cos (1)*sin(1)   5*cos(1)*sin(1)   5*cos (1)*sin(1)
-- + -------------- + --------------- + ----------------
16         6                 16                24
sin⁡(1)cos⁡5(1)6+5sin⁡(1)cos⁡3(1)24+5sin⁡(1)cos⁡(1)16+516\frac{\sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{6} + \frac{5 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{24} + \frac{5 \sin{\left(1 \right)} \cos{\left(1 \right)}}{16} + \frac{5}{16} 
5/16 + cos(1)^5*sin(1)/6 + 5*cos(1)*sin(1)/16 + 5*cos(1)^3*sin(1)/24
Numerical answer [src] 
0.488686178391591
0.488686178391591
The graph
Integral of cos(x)^6 dx

    Use the examples entering the upper and lower limits of integration.

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