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Integration Techniques

Integration U-substitution - Given U


Using the substitution lnx=t,\ln x=t, which of the following is equal to ee63(lnx)2xdx?\int_{e}^{e^{6}} \frac{3(\ln x)^2}{x} dx ?

Evaluate 0312x+6x2+x+1dx.\displaystyle{\int_0^{3}\frac{12x+6}{x^2+x+1}dx.}

Using the substitution u=sinx,u=\sin x, evaluate 0π2sin10xcosxdx.\displaystyle{\int_0^\frac{\pi}{2}\sin^{10} x\cos xdx.}

Evaluate 0π323tan8xdx.\displaystyle{\int_0^\frac{\pi}{32}3\tan8xdx.}

Using the substitution u=ex2,u=e^{x^2}, evaluate 0312xex2dx.\displaystyle{\int_0^{3}12x e^{x^2}dx.}


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