Integration by parts

2011-03-26 4:52 am
Evaluate ∫x(2^x) dx
更新1:

Can you explain more how ∫x(2^x) dx = (1/ln2) ∫ x d(2^x)

回答 (1)

2011-03-26 5:42 am
✔ 最佳答案
∫ x(2^x) dx

= (1/ln2) ∫ x d(2^x)

= (1/ln2)[x(2^x) - ∫ (2^x) dx]

= (1/ln2)[x(2^x) - (1/ln2)(2^x)]

= 2^x(xln2 - 1)/(ln2)^2





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