what is the integral of x√x-2

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Let u2=x-2, x=u2+2 and 2udu/dx=1, so dx can be replaced by 2udu:

∫x√(x-2)dx=∫(u2+2)u.2udu=2∫(u4+2u2)du=2(u5/5+2u3/3)+C=2u3(u2/5+2/3). C is the integration constant.

Replacing u:

2(x-2)3/2((x-2)/5+2/3)+C=2(x-2)3/2(3x+4)/15+C.

by Top Rated User (1.2m points)

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