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Question : 9 of 160
Marks:
+1,
-0
Solution:
I= Substitute:
u=1+ln(x)‌=‌⇒du=‌‌dx⇒dx=xdu=∫‌xduSimplify
‌x:‌=∫‌duAdjust integral boundaries:
x=1‌‌⇒u=1x=e2⇒u=3=‌du Apply exponent rule:
‌=a−b‌=u−2=u−2duApply the Power Rule:
∫xa‌dx=‌,‌‌a≠−1=[‌]13Simplify
‌:‌‌−‌ =[−‌]13 f(x)‌dx=F(b)−F(a)=(F(x))−(F(x))(−‌)=−1(−‌)=−‌=−‌−(−1)Simplify
−‌−(−1):‌=‌
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