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9 wrz 2024 · Rule: Integrals of Exponential Functions. Exponential functions can be integrated using the following formulas. ∫exdx = ex + C (5.6.1) ∫axdx = ax ln a + C (5.6.2) Example 5.6.1: Finding an Antiderivative of an Exponential Function. Find the antiderivative of the exponential function e−x. Solution.
Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. Type in any integral to get the solution, steps and graph.
Choose the specific calculus operation you want to perform, such as differentiation, integration, or finding limits. Once you've entered the function and selected the operation, click the 'Go' button to generate the result.
Integrate the expression in u and then substitute the original expression in x back into the u integral:
3. Integration: The Exponential Form. by M. Bourne. By reversing the process in obtaining the derivative of the exponential function, we obtain the remarkable result: `int e^udu=e^u+K` It is remarkable because the integral is the same as the expression we started with. That is, `e^u`. Example 1 `int3e^(4x)dx` Answer
The following problems involve the integration of exponential functions. We will assume knowledge of the following well-known differentiation formulas : where a is any positive constant not equal to 1 and is the natural (base e) logarithm of a .
4 dni temu · Let E_1(x) be the En-function with n=1, E_1(x) = int_1^infty(e^(-tx)dt)/t (1) = int_x^infty(e^(-u)du)/u. (2) Then define the exponential integral Ei(x) by E_1(x)=-Ei(-x), (3) where the retention of the -Ei(-x) notation is a historical artifact.
