$(1)$ \begin{align} dx=d_1+\frac{d_2-d_1}{l}x\\ \end{align} $(2)$ \begin{align} d\phi&=\frac{Tdx}{GI_p}\\ &=\frac{32Tdx}{G\pi dx^4}\\ &=\frac{32T}{G\pi}\left(d_1+\frac{d_2-d_1}{l}x\right)^{-4}dx \end{align} $(3)$ \begin{align} \phi&=\int_0^ld\phi\\ &=\frac{32T}{G\pi}\int_0^l\left(d_1+\frac{d_2-d_1}{l}x\right)^{-4}dx\\ &=\frac{32T}{G\pi}\left[-\frac{l}{3\left(d_2-d_1\right)}\left(d_1+\frac{d_2-d_1}{l}x\right)^{-3}\right]_0^l\\ &=\frac{32T}{G\pi}\frac{l\left({d_2}^3-{d_1}^3\right)}{3{d_2}^3{d_1}^3\left(d_2-d_1\right)} \end{align}