What is the integration of (x+(1/sqrt(x)) ) ^2?
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Ans: (x+1/sqrt(x) ) ^2 = x^2 + 2sqrt(x) + 1/x
hence the integral is = (x^3)/3 + 4/3(x^(3/2)) + ln(x) + c
hence the integral is = (x^3)/3 + 4/3(x^(3/2)) + ln(x) + c
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It's easiest to just expand:
= x^2 + 2sqrtx + 1/x
Integrate that gives
= x^3/3 +4x^(3/2)/3 + ln|x| + C
= x^2 + 2sqrtx + 1/x
Integrate that gives
= x^3/3 +4x^(3/2)/3 + ln|x| + C