Consider the given integral. #10; #10; I=∫( 2x+3 )^2dx #10; #10; I=∫( 4x^2+9+12x )dx #10; #10; I=4x^33+9x+12x^22+C #10; #10; ...

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Definite Integral as Limit of Sum

Solve ∫ 2x ...

Question

Solve $\int {(2 x + 3)}^{2} d x$

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Solution

Consider the given integral.

$I = \int {(2 x + 3)}^{2} d x$

$I = \int (4 x^{2} + 9 + 12 x) d x$

$I = \frac{4 x^{3}}{3} + 9 x + \frac{12 x^{2}}{2} + C$

$I = \frac{4 x^{3}}{3} + 9 x + 6 x^{2} + C$

Hence, this is the answer.

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