(\integral\_{}^{}\frac{1}{x^{2}}(2x + 1)^{3}dx) = | MATH - FUNDAMENTAL INTEGRATION | SolveeIt

$\int_{}^{}\frac{1}{x^{2}}(2x + 1)^{3}dx$ =

4x² + 12x + 6logx – $\frac{1}{x}$ + c

4x² + 12x – 6logx – $\frac{2}{x}$ + c

2x² + 8x + 3logx – $\frac{2}{x}$ + c

$\text{8}\text{x}^{2}\text{ + 6x + 6logx} + \frac{2}{x} + c$

Answer

4x² + 12x + 6logx – $\frac{1}{x}$ + c

Explanation

(2x + 1)³ dx = $\int_{}^{}\frac{(8x^{3} + 1 + 12x^{2} + 6x)}{x^{2}}$ dx

= $\int \left( 8 x + 12 + \frac { 6 } { x } + \frac { 1 } { x ^ { 2 } } \right)$ dx = 4x² + 12x + 6 logx – $\frac{1}{x}$ +c

Question: \(\int_{}^{}\frac{1}{x^{2}}(2x + 1)^{3}dx\) =...