r2(2+3x.3313.

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Solution

The integral of the function is given as,

∫ x 2 ( 2+3 x 3 ) 3 dx (1)

Consider, 2+3 x 3 =t.

Differentiate with respect to x.

2+3 x 3 =t 9 x 2 dx=dt

Substitute 9 x 2 dx=dt in equation (1) and then integrate.

∫ x 2 ( 2+3 x 3 ) 3 dx = 1 9 ∫ dt t 3 = 1 9 ∫ t −3 dt = 1 9 [ t −2 −2 ]+C = −1 18 ( 1 t 2 )+C

Substitute 2+3 x 3 =t in above equation.

∫ x 2 ( 2+3 x 3 ) 3 dx = −1 18 ( 1 t 2 )+C = −1 18 ( 1 ( 2+3 x 3 ) 2 )+C

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