3x5.+2x

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Solution

The given function is 3x 1+2 x 4 .

Consider, ∫ 3x 1+2 x 4 dx(1)

Also, ∫ 1 a 2 + x 2 = tan −1 x a +c (2)

Now let, 2 x 2 =t 2 2 xdx=dt

Substitute values of t and dt in (1),

∫ 3x 1+2 x 4 dx= 3 2 2 ∫ ( 1 1+ t 2 ) dt = 3 2 2 ( tan −1 t )+c = 3 2 2 ( tan −1 ( 2 x 2 ) )+c By Using (2)

Thus, the integral of the function 3x 1+2 x 4 is 3 2 2 ( tan −1 ( 2 x 2 ) )+c.

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