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To verify an antiderivative, you differentiate the proposed result. If the derivative of the proposed function equals the original integrand, then the proposal is correct.

Conditions: The proposed function is differentiable.; The original integrand is defined on the domain of interest.

To verify an antiderivative, you differentiate the proposed result. If the derivative of the proposed function equals the original integrand, then the proposal is correct.

Conditions: The proposed function is differentiable.; The original integrand is defined on the domain of interest.

Different functions such as $x^2$ and $x^2 + C$ share the same derivative because the derivative measures the slope of the tangent line at each point $x$. Adding a constant $C$ shifts the graph vertically but does not change its steepness or shape.

Conditions: The functions differ only by an additive constant.; The domain is an interval where the derivative exists.

Different functions such as $x^2$ and $x^2 + C$ share the same derivative because the derivative measures the slope of the tangent line at each point $x$. Adding a constant $C$ shifts the graph vertically but does not change its steepness or shape.

Conditions: The functions differ only by an additive constant.; The domain is an interval where the derivative exists.