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Question Number 26909 by sorour87 last updated on 31/Dec/17

$$\int \frac{e^x(\frac{1}{x}-\frac{2}{x^3})}{-2}dx$$

Answered by prakash jain last updated on 31/Dec/17

$$\int e^x(-\frac{1}{2x}+\frac{1}{x^3})dx$$$$\int -\frac{e^x}{2x}dx+\int \frac{e^x}{x^3}dx$$$$integratefirstbyparts$$$$=-\frac{e^x}{2x}-\int \frac{e^x}{2x^2}dx+\int \frac{e^x}{x^3}dx$$$$=-\frac{e^x}{2x}-\frac{e^x}{2x^2}-\int \frac{e^x}{x^3}dx+\int \frac{e^x}{x^3}dx$$$$=-\frac{e^x(x+1)}{2x^2}$$

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