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Question

Evaluate :
x5x2+9dx

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Solution

Consider the given integral.


I=x5x2+4dx



Let t=x2+4


dtdx=2x+0


dt2=xdx



Therefore,


I=12(t4)2tdt


I=12t2+168ttdt


I=12(t+16t8)dt


I=12[t22+16log(t)8t]+C



On putting the value of t, we get


I=12(x2+4)22+16log(x2+4)8(x2+4)+C



Hence, this is the answer.


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