SeC integral (sec integral derivation process)

The indefinite integral of secx is Ln1 + sinxln1 sinx2 +Csec is the ratio of the hypotenuse of a right triangle to the adjacent edge of an acute angle, and is the reciprocal of the cosine, that is, secx=1cosx. If 1=sinx^2+cosx^2 in this equation is substituted, we can get that secx=sinxtanx+cosxsecx = 1cosx. Secx is a secant function, which is the ratio of the hypotenuse of a right triangle to the adjacent edge of an acute angle.

Indefinite integral calculation method 1 The integral formula method directly uses the integral formula to calculate the indefinite integral 2 The substitution integral method can be divided into the first type of substitution method and the second type of substitution method 1 The first type of substitution method is the differentiation method. Finally, relying on a certain integral formula to obtain the original indefinite integral 2 The second type of substitution method is often used to eliminate the roots in the integrand.

2 When calculating the integral of secx, the trigonometric identity conversion method is usually used to convert secx into a more familiar trigonometric function form for processing. The key formula involved is the relationship between secx and tanx, that is, secsup2x = 1 + tansup 2x3 It is deduced using the integral properties. Through a series of identity transformations, the integral result of secx is finally obtained as lnsecx + tanx + C where C is.

secx=1cosx The reasoning process secx=1cosx = sec x sec is a trigonometric function. The so-called secant function is the ratio of the hypotenuse of a right triangle to the adjacent edge of an acute angle, and the reciprocal of the cosine, that is, secx=1cosx If you substitute 1=sinx^2+cosx^2 in this equation, you can get secx=sinxtanx+cosx.

whenSEC integrationWhen we set vlt to dxlt, we have\\int secx dx = secx \cdot x \int x \cdot tanxsecx dx\lt Next, we focus on the next step of integration. For\\int x \cdot tanxsecx dx\lt, we use the partial integration method again, let u=xlt, dv=secxtanxdxlt, and so on.

The analytical process understanding the topic requires solving the indefinite integral conversion form of sectdt First, we convert sectdt to $frac1cos tdt$, so that its integral form is easier to see. Next, we try to convert it to expressions related to $sin t$and $cos t$, so that we can integrate using the triangular identity Using the triangular identity we know that $frac1cos ^2t =.

Note that if derivative is regarded as an operation, then integration is its inverse operation, that is, if fx is known, you need to find a function Fx such that F#39x=fx, so relatively speaking, integration is more difficult than derivative. 2 Uncertain rule of integration 3 Basic trigonometric function relationship sinα·cscα=1 cosα·secα=1 tanα·cotα=1 sin#178α+cos#178α=1 sec#178αtan#.

There are many definite integral expressions for secxdx. One common form is\J\sec x\, dx=\ln\sec x+\tan x+C\When using triangular substitution t=\sin x, the integral can be converted to\I=\ln\left\frac1+\sin x1\sin x\right+C\, which is then simplified to\H=\frac12\ln\left\frac1+\sin x1\sin x\.

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02GPCSEC integration requirements In narrow scale correction, the integration of the standard sample spectrum is to obtain the retention time of the peak apex. The requirements for integration settings are not very strict. However, the sample spectrum.

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