There are multiple formulas for the integral of sec x. But the most popular formula that we use is ∫ sec x dx = ln |sec x + tan x| + C, where C is the integration constant.

2024年11月24日 · 前三种较为常见,最后一种较为少见. \text {第一种:}\displaystyle \int \sec x \mathrm {d}x=\displaystyle\int\frac {\cos x} {1-\sin^2 x}\mathrm {d}x=\frac {1} {2}\displaystyle\int \frac {1} {1+\sin x}+\frac {1} {1-\sin x}\mathrm {d} (\sin x)=\frac {1} {2} (\mathrm {ln}^ {|1+\sin x|}-\mathrm {ln}^ {|1-\sin x|})+C\\ \text {第二种 ...

2024年7月26日 · The integral of sec x is ∫ (sec x).dx = ln| sec x + tan x| + C. Integration of the secant function, denoted as ∫ (sec x).dx and is given by: ∫ (sec x).dx = ln| sec (x) + tan (x)| + C. Sec x is one of the fundamental functions of trigonometry and is the reciprocal function of Cos x. Learn how to integrate sec x in this article.

2013年9月27日 · Now let u = tan(x) + sec(x), you get sec(x) = du u, then you integrate both sides: ∴ ∫sec(x) dx = ∫du u = ln | u | + C = ln | tan(x) + sec(x) | + C.

本文目的是想总结形如 \int \sec^n x \cdot \tan^mx\ dx 类问题的通解1、关于 secx,tanx 基础三角变换 sec^2x=tan^2x+1 \frac {d} {dx}\tan x=\sec^2 x\Leftrightarrow\int \sec^2x\ dx=\tan x+C \frac …

Multiply and divide by (sec x + tan x); use Substitution.

2021年8月22日 · 三角积分 求 \int \sin^ {m}x\cos^ {n}x\text { }dx 类积分的策略：若余弦函数的幂为奇数（ n=2k+1 ），则保留一个余弦因数 \cos x 并用 \cos^ {2}x=1-\sin^ {2}x 表示剩余关于 \sin x 的因数： \int \sin^ {m}x\cos^ {2k…

Calculate the indefinite integral of sec (x) with detailed explanations.

Here you will learn proof of integration of secx or sec x and examples based on it. The integration of sec x is log |sec x + tan x| + C or log|tan(π 4 + x 2)| l o g | t a n (π 4 + x 2) | + C. where C is the integration constant. i.e. ∫ ∫ sec x = log |sec x + tan x| + C. or, ∫ ∫ sec x = log|tan(π 4 + x 2)| l o g | t a n (π 4 + x 2) | + C.

Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step