x^(4) dx =
x^(5) /5 [2,4] =>
4^(5)/5 - 2^(5)/5 =>
2^(10) / 5 - 2^(5) / 5
[2^(10) - 2^(5) ] / 5 =
[1024 - 32] / 5 =
992/5 = 198.4
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The integral of x4dx = x5/5 Evaluate that integral from 2 to 4 = 45/5 - 25/5 =(45 - 25)/5 = (1024-32)/5 = 992/5 = 198.4
The integral of arcsin(x) dx is x arcsin(x) + (1-x2)1/2 + C.
Integral( sin(2x)dx) = -(cos(2x)/2) + C
dy/dx = 3 integral = (3x^2)/2
Integrate by parts: ∫ uv dx = u ∫ v dx - ∫ (u' ∫ v dx) dx Let u = -2x Let v = cos 3x → u' = d/dx -2x = -2 → ∫ -2x cos 3x dx = -2x ∫ cos 3x dx - ∫ (-2 ∫ cos 3x dx) dx = -2x/3 sin 3x - ∫ -2/3 sin 3x dx = -2x/3 sin 3x - 2/9 cos 3x + c
integration by parts. Let u=lnx, dv=xdx-->du=(1/x)dx, v=.5x^2. Integral of (xlnxdx)=lnx*.5x^2-integral of .5x^2(1/x)dx=lnx*.5x^2-integral of .5xdx=lnx*.5x^2-(1/6)x^3. That's it.