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Evaluate `int_e^(e^4)dx/(xsqrt(lnx))` . I can only get a 3 but the answer says it...

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user6978788 | Student, Undergraduate | (Level 1) Honors

Posted February 7, 2013 at 9:25 PM via web

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Evaluate `int_e^(e^4)dx/(xsqrt(lnx))` . I can only get a 3 but the answer says it should be 2

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tiburtius | High School Teacher | (Level 3) Associate Educator

Posted February 7, 2013 at 10:01 PM (Answer #1)

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`int_e^(e^4)(dx)/(x sqrt(lnx))=|(t=lnx),(dt=(dx)/x),(t_1=ln e=1),(t_2=ln e^4=4)|=`

We have made substitution which means we also need to change limits of our integral to `t_1` and `t_2`.

`int_1^4(dt)/(sqrt t)=2sqrt t |_1^4=2sqrt4-2sqrt1=2cdot2-2cdot1=2`

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