`int (5+4x^2)^2 dx` Find the indefinite integral

`int (5+4x^2)^2dx`

To solve, expand `(5+4x^2)^2` .

`= int [(5+4x^2)(5+4x^2)]dx`

`= int (25+20x^2+20x^2+16x^4)dx`

`= int (25+40x^2+16x^4)dx`

To evaluate this integral, use the formulas:

• `int adx = ax + C` 


• `int x^n dx = x^(n+1)/(n+1) + C`

Applying the formulas, it results to

`= 25x + (40x^3)/3 + (16x^5)/5 + C`

Therefore, `int (5+4x^2)^2dx =25x + (40x^3)/3 + (16x^5)/5 + C` .