Evaluate the integral: {eq}\; \int \tan^2(x) \sec(x) \, \mathrm{d}x {/eq}. Integration in Calculus: Integration techniques can be used to find antiderivatives of a trigonometric function. Sometimes trigonometric identities may be needed to do so. ...
Integral of sec(x)*tan(x) by x: 1/cos(x)+C To compute the integral of sec(x) * tan(x) with respect to x, follow these steps: 1.Identify the integral: We want to compute the integral 2.Recall the derivative: Recognize that the derivative of sec(x) is sec(x) * tan(x). Th...
{eq}\frac{1-\tan 2x}{\sec 2x} \mathrm{d}x {/eq}. Integration: Here, in our problem we have to evaluate the integral. Firstly, we try to simplify the given integral by applying the various trigonometry ratios: {eq}\tan (x)=\dfrac{\sin (x)}{\cos (x)}\\ \sec x=\dfrac...
{eq}\int \frac {\sec^{2} x \tan^{2} x}{\sqrt {9 - \tan^{2} x}} dx {/eq} To simplify this integral, we can use a substitution where: {eq}u = \tan... Learn more about this topic: Integration by Substitution Steps & Examples ...
Find the integral: integral(sec x(sec x + tan x))dx Find the integral of (sec x tan x)dx. Find the integral (dx) / (cos^2x sqrt (1+ tan x)). Find the integral of 3sec^3(x) tan^2(x) dx. Integrate: integral tan\ 4x dx ...
Split the single integral into multipleintegrals. (∫ (sec)(x)dx+∫ (tan)(x)dx) The integral of ( (sec)(x)) with respect to ( x) is ( (ln)(|(sec)(x)+(tan)(x)|)). ( (ln)(|(sec)(x)+(tan)(x)|)+C+∫ (tan)(x)dx) The integral of ( (tan)(x)) with respect...
dtdx=sec2x⇒dt=sec2xdxThis means we can replace sec2xdx with dt. Step 2: Rewrite the IntegralNow, we can rewrite the integral in terms of t:∫sec2x√tan2x+4dx=∫1√t2+4dt Step 3: Recognize the Integral FormThe integral ∫1√t2+a2dt has a standard result:∫1√t2+a2dt=ln|t...
∫sec2x9−tan2xdx View Solution Evaluate∫sec2x(1+tanx)2dx View Solution ∫sec2x1+tanxdx View Solution Evaluate∫x3(sec2x−tan2x)dx View Solution Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Clas...
How to solve∫tan3(x)dx? https://math.stackexchange.com/q/20074 One standard approach to integral involving powers of tangent is the following: Rewrite your power as something timestan2(x). In this case:tan3(x)=tan(x)⋅tan2(x). Now, use thattan2(x)=sec2(x)−1... ...
1+tan^2 x = sec^2 x integral of sec^2 x dx = tan x + c