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Question

dx(x+100)x+99=f(x)+cf(x)=

A
2(x+100)1/2
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B
3(x+100)1/2
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C
2tan1(x+99)
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D
2tan1(x+100)
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Solution

The correct option is D 2tan1(x+99)
dx(x+100)x+99
=2dx2x+99(1+(x+99)2)
=2d(x+99)(1+(x+99)2)
=2tan1(x+99)+c [ Where c is integrating constant]
Comparing this with gives equation we get,
f(x)=2tan1(x+99).

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