The line should be ∫ 0 t Ξ − 1 ( τ ) g ( τ ) d τ = ∫ 0 t [ − 1 2 1 2 e − 2 τ ] d τ = [ − 1 2 t 1 4 ( 1 − e − 2 t ) ] . {\displaystyle \int _{0}^{t}\Xi ^{-1}(\tau )g(\tau )d\tau =\int _{0}^{t}\left[{\begin{array}{c}-{\frac {1}{2}}\\{\frac {1}{2}}e^{-2\tau }\end{array}}\right]d\tau =\left[{\begin{array}{c}-{\frac {1}{2}}t\\{\frac {1}{4}}\left(1-e^{-2t}\right)\end{array}}\right].}
![{\displaystyle \int _{0}^{t}\Xi ^{-1}(\tau )g(\tau )d\tau =\int _{0}^{t}\left[{\begin{array}{c}-{\frac {1}{2}}\\{\frac {1}{2}}e^{-2\tau }\end{array}}\right]d\tau =\left[{\begin{array}{c}-{\frac {1}{2}}t\\{\frac {1}{4}}\left(1-e^{-2t}\right)\end{array}}\right].}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6efb516d7a5db744f002c3322b93dfd8fb08740d)
