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

Step-by-step solution

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