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Let $Z_t=\int_{0}^{t} W_s ds$. Use integration by parts to show that $Z_t=\int_{0}^{t} (t-s) dW_s$. I have tried and i can't get the answer.

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Note that \begin{align*} d(sW_s) = sdW_s + W_s ds. \end{align*} Then you can integrate on both sides.

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