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## Main Question or Discussion Point

My friends were discussing about this problem (which they made up themselves).

∫[itex]\frac{1}{x^{2}+25}[/itex]d[itex]x^{2}[/itex]

They were substituting x^2 for y ([itex]x^{2}[/itex]=y) and thus the answer would come to be log(y+25)

that is log([itex]x^{2}[/itex]+25)

I don't think this is the case , i guess that we would be differentiating wrt a 2nd degree curve like a parabola in case of this problem .

Would you people point out whats the real thing.

∫[itex]\frac{1}{x^{2}+25}[/itex]d[itex]x^{2}[/itex]

They were substituting x^2 for y ([itex]x^{2}[/itex]=y) and thus the answer would come to be log(y+25)

that is log([itex]x^{2}[/itex]+25)

I don't think this is the case , i guess that we would be differentiating wrt a 2nd degree curve like a parabola in case of this problem .

Would you people point out whats the real thing.