Practicing Success
Practicing Success
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| \(\int \frac{1}{4x^2 +4x+5}dx\) |
\(\frac{4}{\tan^{-1}\left(x+\frac{1}{2}\right)}+c\) \(\frac{1}{4}\tan^{-1}\left(x+\frac{1}{2}\right)+c\) \(\frac{1}{4}\tan^{-1}\left(x-\frac{1}{2}\right)+c\) \(\tan^{-1}\left(x-\frac{1}{2}\right)+c\) |
| \(\frac{1}{4}\tan^{-1}\left(x+\frac{1}{2}\right)+c\) |
| \(\begin{aligned}4x^2+4x+5&=4\left[\left(x+\frac{1}{2}\right)^{2}+1\right]\\ \int \frac{1}{4x^2+4x+5}dx&=\frac{1}{4}\int \frac{dx}{\left(x+\frac{1}{2}\right)^{2}+1}\\ &=\frac{1}{4}\tan^{-1}\left(x+\frac{1}{2}\right)+c\end{aligned}\) |
