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which was to be derived. [2] A possible mnemonic is: "The integral of secant cubed is the average of the derivative and integral of secant". Reduction to an integral of a rational function
A standard method of evaluating the secant integral presented in various references involves multiplying the numerator and denominator by sec θ + tan θ and then using the substitution u = sec θ + tan θ. This substitution can be obtained from the derivatives of secant and tangent added together, which have secant as a common factor. [6]
The following is a list of integrals (antiderivative functions) of trigonometric functions.For antiderivatives involving both exponential and trigonometric functions, see List of integrals of exponential functions.
The HP-45 is the second scientific pocket calculator introduced by Hewlett-Packard, adding to the features of the HP-35. It was introduced in 1973 [1] with an MSRP of US$395 [2] (equivalent to $2,711 in 2023). [3] Especially noteworthy was its pioneering addition of a shift key that gave other keys alternate functions.
The TI-83 was the first calculator in the TI series to have built-in assembly language support. The TI-92, TI-85, and TI-82 were capable of running assembly language programs, but only after sending a specially constructed (hacked) memory backup. The support on the TI-83 could be accessed through a hidden feature of the calculator.
The TI-36X series is one of the few calculators [5] currently permitted for use on the Fundamentals of Engineering exam. While TI offers other calculators eligible for use on the exam, the TI-36X Pro is the most feature full Texas Instruments calculator permitted. HP and Casio also make calculators permitted on the exam.
The restriction on Arg(x) is to avoid a discontinuity (shown as the orange vs blue area on the left half of the plot above) that arises because of a branch cut in the standard logarithm function ( ln ). Ci(x) is the antiderivative of cos x / x (which vanishes as ).
2 Integrals involving only hyperbolic cosine functions. 3 Other integrals. Toggle Other integrals subsection. 3.1 Integrals of hyperbolic tangent, cotangent, secant, ...