∫ 2 x - 3 3 x + 2 d x =

Question

∫ 2 x - 3 3 x + 2 d x =, 2 135 54 x 2 - 123 x + 106 3 x + 2 + c, 2 135 54 x 2 + 123 x - 106 3 x + 2 + c, 2 135 54 x 2 - 123 x - 106 3 x + 2 + c, 2 135 54 x 2 - 195 x - 106 3 x + 2 + c

MARKS App · Accepted Answer

Let I = ∫ 2 x - 3 3 x + 2 d x Put 3 x + 2 = t 2 ⇒ d x = 2 t 3 d t ∴ I = ∫ 2 t 2 - 2 3 - 3 × t × 2 t 3 d t ⇒ I = 2 9 ∫ 2 t 4 - 13 t 2 d t ⇒ I = 2 9 2 t 5 5 - 13 t 3 3 + c ⇒ I = 2 135 6 t 5 - 65 t 3 + c ⇒ I = 2 135 6 3 x + 2 2 - 65 3 x + 2 3 x + 2 + c ⇒ I = 2 135 54 x 2 - 123 x - 106 3 x + 2 + c

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