Find the indefinite integral. {eq}\displaystyle \int \sec 2 x \tan 2 x\ dx {/eq} Integration by Substitutions: In calculus, integration is a method of collecting all antiderivatives of a function. In the substitution method of integration, the given integral is transformed into a si...
Integrate: ∫sec2xtanxdx Indefinite Integral: The integration of the given function can be solved using the method of substitution, which simplifies the integrand, thus making it easier to integrate. Answer and Explanation: The given integral is: ∫sec2xtanxdx Now it can ...
tan2x=sec2x−1. Using this identity, we can rewrite the integral: ∫(tanx−x)(sec2x−1)dx. This expands to: ∫(tanx−x)sec2xdx−∫(tanx−x)dx. Step 3: Evaluate the First IntegralWe will focus on the first integral: ∫(tanx−x)sec2xdx. To solve this, we can use ...
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...
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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...
Given ∫7tan5xsec2xdx, let tanx=t. Then sec2xdx=dt. Hence we must have I=7∫t5dt=76t6+c=67tan6x+c where c is constant. Evaluate an integral involving tangent and secant: ∫tan2xsec2xdx https://math.stackexchange.com/questions/937443/evaluate-an-integra...
代數輸入 三角輸入 微積分輸入 矩陣輸入 ∫tan(x)2dx 評估 tan(x)−x+С 對x 微分 (cos(x))21−1
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Evaluate∫tan(3x)sec2(3x)etan2(3x)dx. Evaluating integrals with substitution In this problem we are asked to evaluate an integral composed of trig functions. We will be using ausubstitution technique to help integrate. ∫f(g(x))g′(x)dx=∫f(u)duwhenu=g(x) ...