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25Integration by Parts - University of California, Berkeley
math.berkeley.edudv =ex dx (Exponential function) du =cosx dx v =∫ex dx =ex ∫ex cosx dx =ex cosx + (uv−∫vdu) ∫ex cosx dx =ex cosx + sin x ex −∫ex cosx dx Note appearance of original integral on right side of equation. Move to left side and solve for integral as follows: 2∫ex cosx dx = ex cosx + ex sin x + C ∫ex x dx = (ex cosx + ex sin x) + C ...