If ∫ ( x ) 5 d x ( x ) 7 + x 6 = λ log x 9 x 9 + 1 + C , then a + λ equal to

Question

If ∫ ( x ) 5 d x ( x ) 7 + x 6 = λ log x 9 x 9 + 1 + C , then a + λ equal to, 2, > 2, 2, > 3

MARKS App · Accepted Answer

Let I = ∫ d x x 2 + x 7 = ∫ d x x 7 1 ( x ) 5 + 1 Put 1 + 1 x 5 = t ⇒ - 5 2 · 1 ( x ) 7 d x = d t ∴ I = - 2 5 ∫ d t t = - 2 5 log t + C = - 2 5 log 1 + 1 x 5 + C = - 2 5 log x 5 / 2 + 1 x 5 / 2 + C ⇒ λ = - 2 5 and a = 5 2 ∴ a + λ = 2 . 1 > 2

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