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Question

x2 dx(a+bx)2=

A
1b2[x+2ablog(a+bx)a2b1(a+bx)]
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B
1b2[x2ablog(a+bx)+a2b1(a+bx)]
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C
1b2[x+2ablog(a+bx)+a2b1(a+bx)]
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D
1b2[x+ab2ablog(a+bx)a2b1(a+bx)]
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Solution

The correct option is D 1b2[x+ab2ablog(a+bx)a2b1(a+bx)]
Put a+bx=tx=tab and dx=dtb
I=(tab)2×1t2dtb
=1b3(12at+a2.t2)dt=1b3[t2a log ta2t]
=1b2[x+ab2ablog(a+bx)a2b1(a+bx)]

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