The value of x^ 2 d x (x^ 2 +a^ 2 ) (x^ 2 +b^ 2 ) is

Mathematics · JEE Main · NTA Exams — Integral Calculus

1. \(\frac{1}{b^{2}-a^{2}}\left[b \tan ^{-1} \frac{x}{b}-a \tan ^{-1} \frac{x}{a}\right]+C\)
2. \(\frac{1}{b^{2}-a^{2}}\left[a \tan ^{-1} \frac{x}{b}-b \tan ^{-1} \frac{x}{a}\right]+C\)
3. \(\frac{1}{b^{2}-a^{2}}\left[b \tan ^{-1} \frac{x}{b}+a \tan ^{-1} \frac{x}{a}\right]+C\)
4. none of these

Answer

(A) 1 b^ 2 -a^ 2 [b ^ -1 x b -a ^ -1 x a ]+C

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