Definite Integration

\(2 \tan ^{-1} 2+\frac{1}{2} \log _e\left(\frac{5}{4}\right)+\frac{\pi}{2}\)

\(2 \tan ^{-1} 2+\frac{1}{2} \log _e\left(\frac{5}{4}\right)-\frac{\pi}{2}\)

\(2 \tan ^{-1} 2-\frac{1}{2} \log _e\left(\frac{5}{4}\right)+\frac{\pi}{2}\)

\(2 \tan ^{-1} 2-\frac{1}{2} \log _e\left(\frac{5}{4}\right)-\frac{\pi}{2}\)