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         intagrate      x5/2     dx=alog( xk)
x7/6+x6                (1+xk)
8 years ago

Jitender Singh
IIT Delhi
158 Points
										Ans: 5/2$I = \int \frac{x^{5/2}}{x^{6}+x^{7/2}}dx$$t = \sqrt{x}$$dt = \frac{1}{2\sqrt{x}}dx$$I = 2\int \frac{1}{t(t^{5}+1)}dt$$s = t^{5}$$ds = 5t^{4}dt$$I = \frac{2}{5}\int \frac{1}{s(s+1)}ds$$I =\frac{2}{5}log(\frac{s}{s+1}) +constant$$I =\frac{2}{5}log(\frac{t^{5}}{t^{5}+1}) +constant$$I =\frac{2}{5}log(\frac{x^{5/2}}{x^{5/2}+1}) +constant$k = 5/2Thanks & RegardsJitender SinghIIT DelhiaskIITians Faculty

3 years ago
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