What is the integration of (x+1/sqrt(x) ) ^2?

👨🏻‍🏫 學術台數學

MandM

2011-06-19 8:29 am

What is the integration of (x+(1/sqrt(x)) ) ^2?

更新1:

what if replace x by 4 first and 1 second and then minus

回答 (2)

[匿名]

2011-06-19 8:56 am

✔ 最佳答案

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

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[匿名]

2011-06-19 3:38 pm

It's easiest to just expand:

= x^2 + 2sqrtx + 1/x

Integrate that gives

= x^3/3 +4x^(3/2)/3 + ln|x| + C

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