I need help to solve The partial fraction to solve this problem. I do know how he solved the partial fraction only but I know rest of the solution.&nbsp;

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I need help to solve The partial fraction to solve this problem. I do know how he solved the partial fraction only but I know rest of the solution.&amp;nbsp;

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∫exx2+1dxLet&#039;s begin by using integration by parts. Let u=12ex and dv=dxx2+1. Then du=12exdx and v=tan−1(x). Using the formula for integration by parts, we have:∫exx2+1dx=12extan−1(x)−∫12extan−1(x)dxNow we need to evaluate the second integral. We can do this by using integration by parts again. Let u=tan−1(x) and dv=12exdx. Then du=1x2+1dx and v=12ex. Using the formula for integration by parts again, we get:∫12extan−1(x)dx=12extan−1(x)−∫12(x2+1)exdxWe can now substitute this back into our original integral to get:∫exx2+1dx=12extan−1(x)−(12extan−1(x)−12∫exx2+1dx)Simplifying, we get:∫exx2+1dx=12(extan−1(x)+C)where C is the constant of integration.Therefore, the solution is 12(extan−1(x)+C).

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