First slide

Integration

Question

Integrate the following functions with respect to x
$\int (6 x + 2)^{3} d x$

Moderate

A

$\frac{(6 x + 2)^{4}}{24} + c_{2}$
B

$\frac{(6 x + 2)^{4}}{25} + c_{2}$
C

$\frac{(6 x + 2)^{2}}{24} + c_{2}$
D

$\frac{(3 x + 2)^{4}}{24} + c_{2}$

Solution

$\int (6 x + 2)^{3} d x = \frac{1}{6} \int X^{3} d x W h e r e, X = 6 x + 2 = \frac{1}{6} (\frac{X^{4}}{4}) + c_{1} = \frac{(6 x + 2)^{4}}{24} + c_{2}$

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