The integral ∫ 2 x 12 + 5 x 9 x 5 + x 3 + 1 3 d x , is equal to

Question

The integral ∫ 2 x 12 + 5 x 9 x 5 + x 3 + 1 3 d x , is equal to, x 5 2 x 5 + x 3 + 1 2 + c, - x 10 2 x 5 + x 3 + 1 2 + c, - x 5 x 5 + x 3 + 1 2 + c, x 10 2 x 5 + x 3 + 1 2 + c

MARKS App · Accepted Answer

Given, I = ∫ 2 x 12 + 5 x 9 x 5 + x 3 + 1 3 d x = ∫ 2 x 12 + 5 x 9 d x x 15 1 + 1 x 2 + 1 x 5 3 = ∫ 2 x 3 + 5 x 6 d x 1 + 1 x 2 + 1 x 5 3 Let, 1 + 1 x 2 + 1 x 5 = t ⇒ - 2 x 3 - 5 x 6 d x = d t ⇒ 2 x 3 + 5 x 6 d x = - d t I = - ∫ d t t 3 = 1 2 . t 2 I = 1 2 1 1 + 1 x 2 + 1 x 5 2 + c = 1 2 x 10 x 5 + x 3 + 1 2 + c Where c is the constant of integration. = x 10 2 x 5 + x 3 + 1 2 + c

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