Practicing Success
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$∫\frac{x+e^{2x}}{x^2+e^{2x}}=$ |
$log|x^2+e^{2x}|+C$ $\frac{1}{2}log|x^2+e^{2x}|+C$ $\frac{1}{2}log|x^2|+C$ $log|e^{2x}|+C$ |
$\frac{1}{2}log|x^2+e^{2x}|+C$ |
The correct answer is Option (2) → $\frac{1}{2}log|x^2+e^{2x}|+C$ $I=∫\frac{x+e^{2x}}{x^2+e^{2x}}dx$ let $y=x^2+e^{2x}$ $dy=2x+2e^{2x}dx$ so $\frac{dy}{2}=x+e^{2x}dx$ $I = \frac{1}{2}\int\frac{dy}{y}=\frac{1}{2}\log y +C$ $=\frac{1}{2}\log(x^2+e^{2x})+C$ |
