3x21.x +1

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Solution

The given function is 3 x 2 x 6 +1 .

Consider, ∫ 3 x 2 x 6 +1 dx(1)

Let, x 3 =t 3 x 2 dx=dt

Substitute values of t and dt in (1),

∫ 3 x 2 x 6 +1 dx= ∫ dt t 2 +1 = tan −1 ( t )+c = tan −1 ( x 3 )+c

Thus, the integral of the function 3 x 2 x 6 +1 is tan −1 ( x 3 )+c.

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