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(A) To find the anti-derivative of $f(x) = 3x^{2} + 4x^{3}$ by the method of inspection,we look for a function $F(x)$ such that $F'(x) = f(x)$.We know

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$x^{3} + x^{4}$

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(A) To find the anti-derivative of $f(x) = 3x^{2} + 4x^{3}$ by the method of inspection,we look for a function $F(x)$ such that $F'(x) = f(x)$.We know that the derivative of $x^{n}$ is $nx^{n-1}$.For the first term $3x^{2}$,we observe that $\frac{d}{dx}(x^{3}) = 3x^{2}$.For the second term $4x^{3}$,we observe that $\frac{d}{dx}(x^{4}) = 4x^{3}$.By the linearity property of derivatives,we have:$\frac{d}{dx}(x^{3} + x^{4}) = \frac{d}{dx}(x^{3}) + \frac{d}{dx}(x^{4}) = 3x^{2} + 4x^{3}$.Therefore,an anti-derivative of $3x^{2} + 4x^{3}$ is $x^{3} + x^{4}$.

Find an anti-derivative for the following function using the method of inspection:
$3x^{2} + 4x^{3}$

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Find an anti-derivative for the following function using the method of inspection:$3x^{2} + 4x^{3}$