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Question

dx5x22x

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Solution

We have,

dx5x22x

dx5x225x


Making perfect square and we get,

dx5x225x+(15)2(15)2

15dx(x15)2(15)2


Using formula,

dxx2a2=lnx+x2a2


Therefore,

15dx(x15)2(15)2=15ln∣ ∣(x15)+(x15)2(15)2∣ ∣

=15ln(x15)+5x22x


Hence, this is the answer.


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