# Math Help - One more integral substitution

1. ## One more integral substitution

Use a substitution x=f(t) to transform

integral (0 to 1) x/(x+1) dx into

integral (0 to infinity) t/((2t+1)*(t+1)^2 dt

Thanks

1) put $x=\frac1u$ and your integral becomes $\int_{1}^{\infty }{\frac{du}{u^{2}(u+1)}}.$
2) put $v=u-1$ and your integral becomes $\int_0^\infty\frac{dv}{(v+1)^2(v+2)}.$
3) put $v=\frac1t$ and your integral becomes $\int_0^\infty\frac t{(1+2t)(t+1)^2}\,dt,$ and we're done.