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Using the substitution lnx=t,\ln x=t,lnx=t, which of the following is equal to ∫ee63(lnx)2xdx?\int_{e}^{e^{6}} \frac{3(\ln x)^2}{x} dx ?∫ee6x3(lnx)2dx?
Evaluate ∫0312x+6x2+x+1dx.\displaystyle{\int_0^{3}\frac{12x+6}{x^2+x+1}dx.}∫03x2+x+112x+6dx.
Using the substitution u=sinx,u=\sin x,u=sinx, evaluate ∫0π2sin10xcosxdx.\displaystyle{\int_0^\frac{\pi}{2}\sin^{10} x\cos xdx.}∫02πsin10xcosxdx.
Evaluate ∫0π323tan8xdx.\displaystyle{\int_0^\frac{\pi}{32}3\tan8xdx.}∫032π3tan8xdx.
Using the substitution u=ex2,u=e^{x^2},u=ex2, evaluate ∫0312xex2dx.\displaystyle{\int_0^{3}12x e^{x^2}dx.}∫0312xex2dx.
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