Integral 1: $\displaystyle \int_{\frac{1}{2}}^{1}\dfrac{(1 -x)^{7/2}(2x - 1)^{3/2}}{x^7}dx$
Integral 2: $\displaystyle \int_{-\infty}^{\infty}\left(\dfrac{\ln(e^x + 1)}{e^x + 1}\right)^{3}e^x dx$
Integral 1: $\displaystyle \int_{\frac{1}{2}}^{1}\dfrac{(1 -x)^{7/2}(2x - 1)^{3/2}}{x^7}dx$
Integral 2: $\displaystyle \int_{-\infty}^{\infty}\left(\dfrac{\ln(e^x + 1)}{e^x + 1}\right)^{3}e^x dx$