We know that #160; ddx(ax+b)^3=3a(ax+b)^2 ⇒ (ax+b)^2=13addx(ax+b)^3 ⇒ (ax+b)^2 =ddx[13a(ax+b)^3] #160;Thus anti derivative of #160; ( ...

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Sum of Coefficients of All Terms

∫ ax+b2dx

Question

$\int (a x + b)^{2}$ dx

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Solution

We know that $\frac{d}{d x} (a x + b)^{3} = 3 a (a x + b)^{2}$

$\Rightarrow (a x + b)^{2} = \frac{1}{3 a} \frac{d}{d x} (a x + b)^{3}$

$\Rightarrow (a x + b)^{2} = \frac{d}{d x} [\frac{1}{3 a} (a x + b)^{3}]$

Thus anti - derivative of $(a x + b)^{2} i s \frac{1}{3 a} (a x + b)^{3} .$

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