Integral of x^2*cos(x) dx
The solution
Detail solution
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Use integration by parts:
∫udv=uv−∫vdu
Let u(x)=x2 and let dv(x)=cos(x).
Then du(x)=2x.
To find v(x):
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The integral of cosine is sine:
∫cos(x)dx=sin(x)
Now evaluate the sub-integral.
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Use integration by parts:
∫udv=uv−∫vdu
Let u(x)=2x and let dv(x)=sin(x).
Then du(x)=2.
To find v(x):
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The integral of sine is negative cosine:
∫sin(x)dx=−cos(x)
Now evaluate the sub-integral.
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The integral of a constant times a function is the constant times the integral of the function:
∫(−2cos(x))dx=−2∫cos(x)dx
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The integral of cosine is sine:
∫cos(x)dx=sin(x)
So, the result is: −2sin(x)
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Add the constant of integration:
x2sin(x)+2xcos(x)−2sin(x)+constant
The answer is:
x2sin(x)+2xcos(x)−2sin(x)+constant
The answer (Indefinite)
[src]
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| 2 2
| x *cos(x) dx = C - 2*sin(x) + x *sin(x) + 2*x*cos(x)
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∫x2cos(x)dx=C+x2sin(x)+2xcos(x)−2sin(x)
The graph
−sin(1)+2cos(1)
=
−sin(1)+2cos(1)
Use the examples entering the upper and lower limits of integration.