An antiderivative is the inverse operation of a derivative. It is a function that, when differentiated, yields the original function. It is also known as the indefinite integral.
To solve for the antiderivative, you must use integration techniques such as substitution, integration by parts, or partial fractions. These techniques allow you to find an expression for the antiderivative of a given function.
The antiderivative of 2/x is ln|x| + C, where C is a constant. This can be found using the integration technique of substitution, where u = 2/x and du = -2/x^2 dx.
The antiderivative of 5e^5x is e^5x + C, where C is a constant. This can be found using the integration technique of substitution, where u = 5x and du = 5dx.
To solve for the antiderivative of 2/x - 5e^5x, you must use the linearity property of integration to split the function into two separate antiderivatives: the antiderivative of 2/x and the antiderivative of 5e^5x. Then, use the techniques mentioned in previous questions to solve for each antiderivative separately.