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- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/03%3A_Techniques_of_Integration/3.01%3A_Integration_by_PartsThis page provides an overview of integration by parts, a technique used to simplify the integration of products of functions. It includes the formula derived from the product rule, guidance on choosi...This page provides an overview of integration by parts, a technique used to simplify the integration of products of functions. It includes the formula derived from the product rule, guidance on choosing functions with the LIATE mnemonic, and multiple examples ranging from logarithmic to trigonometric integrals. The text also discusses evaluating both definite and indefinite integrals and emphasizes validating results through differentiation.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/03%3A_Techniques_of_Integration/3.03%3A_Trigonometric_SubstitutionThe technique of trigonometric substitution comes in very handy when evaluating integrals of certain forms. This technique uses substitution to rewrite these integrals as trigonometric integrals.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Developmental_Math_(NROC)/18%3A_Exponential_and_Logarithmic_Functions/18.02%3A_Logarithmic_Functions/18.2.02%3A_Properties_of_Logarithmic_FunctionsThere are a number of properties that will help you simplify complex logarithmic expressions. Since logarithms are so closely related to exponential expressions, it is not surprising that the properti...There are a number of properties that will help you simplify complex logarithmic expressions. Since logarithms are so closely related to exponential expressions, it is not surprising that the properties of logarithms are very similar to the properties of exponents. As a quick refresher, here are the exponent properties.
- https://math.libretexts.org/Courses/Hope_College/Math_126_-_Calculus_with_Review_II/01%3A_Inverse_Functions/1.03%3A_Graphs_of_Logarithmic_FunctionsIn this section we will discuss the values for which a logarithmic function is defined, and then turn our attention to graphing the family of logarithmic functions.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/01%3A_Integration/1.07%3A_Integrals_Resulting_in_Inverse_Trigonometric_Functions/1.7E%3A_Exercises_for_Section_1.7This page presents exercises on evaluating integrals, emphasizing inverse trigonometric functions and substitutions. It includes definite integrals with solutions, techniques for finding antiderivativ...This page presents exercises on evaluating integrals, emphasizing inverse trigonometric functions and substitutions. It includes definite integrals with solutions, techniques for finding antiderivatives, and addresses undefined integrals. The text also covers integral calculations involving trigonometric and exponential functions, detailing methods to determine constants for definite integrals.
- https://math.libretexts.org/Courses/Las_Positas_College/Book%3A_College_Algebra/05%3A_Exponential_and_Logarithmic_Functions/5.05%3A_Graphs_of_Logarithmic_FunctionsIn this section we will discuss the values for which a logarithmic function is defined, and then turn our attention to graphing the family of logarithmic functions.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/03%3A_Techniques_of_Integration/3.01%3A_Integration_by_Parts/3.1E%3A_Exercises_for_Section_3.1This page provides exercises focusing on integration techniques, particularly integration by parts and basic methods. It presents specific integrals, suggested u choices, and solved straightforwar...This page provides exercises focusing on integration techniques, particularly integration by parts and basic methods. It presents specific integrals, suggested u choices, and solved straightforward integrals, including definite integrals with exact solutions. Also covered are problems involving areas and volumes from revolving curves and evaluating integrals with exponential, logarithmic, and trigonometric functions, alongside reduction formulas.
- https://math.libretexts.org/Workbench/Algebra_and_Trigonometry_2e_(OpenStax)/06%3A_Exponential_and_Logarithmic_Functions/6.05%3A_Graphs_of_Logarithmic_FunctionsIn this section we will discuss the values for which a logarithmic function is defined, and then turn our attention to graphing the family of logarithmic functions.
- https://math.libretexts.org/Bookshelves/Algebra/Algebra_and_Trigonometry_1e_(OpenStax)/06%3A_Exponential_and_Logarithmic_Functions/6.04%3A_Graphs_of_Logarithmic_FunctionsIn this section we will discuss the values for which a logarithmic function is defined, and then turn our attention to graphing the family of logarithmic functions.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/06%3A_AppendicesContributors and Attributions Gilbert Strang (MIT) and Edwin “Jed” Herman (Harvey Mudd) with many contributing authors. This content by OpenStax is licensed with a CC-BY-SA-NC 4.0 license. Download fo...Contributors and Attributions Gilbert Strang (MIT) and Edwin “Jed” Herman (Harvey Mudd) with many contributing authors. This content by OpenStax is licensed with a CC-BY-SA-NC 4.0 license. Download for free at http://cnx.org.
- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Developmental_Math_(NROC)/18%3A_Exponential_and_Logarithmic_Functions/18.02%3A_Logarithmic_Functions/18.2.01%3A_Introduction_to_Logarithmic_FunctionsThe base of the exponential equation, 11, is also the base (the small subscript number at the end of “log”) in the logarithmic equation. Notice that a larger base makes the graph less steep. (This is ...The base of the exponential equation, 11, is also the base (the small subscript number at the end of “log”) in the logarithmic equation. Notice that a larger base makes the graph less steep. (This is the opposite from exponential functions, where a larger base meant a steeper graph.) A larger base also makes the graph closer to the x-axis for y>0 (or x>1) and closer to the y-axis for y<0 (or x<1).
