is the logarithmic integral function. Details Examples open all Basic Examples(5) Evaluate numerically: In[1]:= Out[1]= Plot over a subset of the reals: In[1]:= Out[1]= Series expansion at the origin: Copy to c
Expanding Logarithmic Expressions: ExamplesThese simple steps work for any expression where there’s a “log” followed by a fraction with terms in the numerator and denominator; You don’t need to memorize any of the rules!. Example question #1: Expand the following logarithmic expression:...
Here are some examples: (1) The Richter magnitude scale measures the intensity of earthquakes. It is calibrated logarithmi- cally to base 10. An earthquake one point higher on the Richter scale is ten times as intense. (2) The pH scale in chemistry is a logarithmic scale to measure the ...
Mittag-Leffler functionsLaplace transformLogarithmic functionEigenfunctionIn this paper, using the Buschman's theorem for the Laplace transform, we show that the logarithmic functions n ( s ) = 1 s ∑ i = 0 n ( 1 ) i n i Γ ( n i ) ( 1 ) ln i ( s ) , n ∈ N , are the ...
Integral Examples & Functions FunctionIntegralExplanation 1/xln |x| + CThe integral of 1/x with respect to x is the natural logarithm of the absolute value of x. 2^x2^x/ln(2) + CUsing the formula for a^x with a = 2. 2xx^2 + CUsing the power rule for integration. ...
Indefinite Integrals; Logarithmic Functions: We observe the derivative of the natural logarithm {eq}\frac{d\ln|x|}{dx}=\frac{1}{x} {/eq}. This suggests the substitution {eq}t=6 - 8x {/eq} since the expression {eq}6 - 8x {/eq} appears in the integrand. We'll need to return ...
Exponential Functions:The integral of an exponential is given by:∫exdx=ex+C Logarithmic Functions:Some cases of integrals yield logarithmic functions.∫axdx=axloga+Cand∫1xdx=log|x|+C Trigonometric Functions:Integration of these may require some substitutions using the var...
Compute definite and indefinite integrals with detailed step-by-step solutions!Integral Calculator Compute the Integral: Try the following examples: [Polynomial Integration] [Trigonometric Integration] [Exponential Integration] [Rational Function Integration] [Linear Function Integration] [Logarithmic Integration...
To integrate trigonometric functions, we can take help of some formulas. ∫tanx=−ln|cosx|+C∫cotx=ln|sinx|+C where, C is the integral constant. Quotient rule of logarithmic function: lnea−lneb=lneab Answer and Explanation: Given: {eq}\...
Tips The one-argument exponential integral is singular atx = 0. The toolbox uses this special value:ei(0) = -Inf. Algorithms The relation betweeneiandexpintis ei(x) = -expint(1,-x) + (ln(x)-ln(1/x))/2 - ln(-x) Both functionsei(x)andexpint(1,x)have a logarithmic singularity...