How do you find the antiderivative of #2/(xsqrtx)#?

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Answer 1 · 2017-12-06T20:59:55

Rewrite it as #2x^(-3/2)# then apply the power rule for antiderivatives.

Add #1# to the exponent and divide by the new exponent.

#2x^(-3/2+1)/(-3/2+1) = 2x^(-1/2)/(-1/2) = -4x^(-1/2)+C#

Check your answer by differentiating.

Perhaps write the answer without negative exponents.

#(-4)/x^(1/2) +C#

Or without rational exponents:

#(-4)/sqrtx +C#