Evaluate {eq}\int \frac {\sec^{2} x \tan^{2} x}{\sqrt {9 - \tan^{2} x}} dx {/eq} Integration by Substitution: Often with integrals, we can make them "more familiar" or "easier" by applying a substitution to the integration variable. By using a substitution, we are s...
Evaluate the integral. Integral of tan x sec^3 x dx. Evaluate the integral: integral 10 dx / 1 + e^x. Evaluate the integral: integral of (sqrt(16x^2 - 25))/(x^3) dx. Evaluate the integral: integral (1 + x^2)^{1 / 2} dx. ...
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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...
Evaluate the integral. {eq}\displaystyle \int \frac {\sec^2 x}{\tan^2 x} \ dx {/eq} Integration by Substitution: If we have to evaluate the integral that has a function in the composite form {eq}\int f(g(x))g'(x)dx {/eq}, one of the best methods that help to ev...
{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...
(∫ (sec)(x)+(tan)(x)dx) 相关知识点: 试题来源: 解析 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+∫...
I=∫π0sec−1(secx)1+tan8xdx we will use the property of definite integrals and some transformations. Step 1: Recognize the Integral and Apply the Property We can use the property of definite integrals: ∫baf(x)dx=∫baf(a+b−x)dx For our case, a=0 and b=π. Thus, we have:...
Write the solution of the differential equation:dy/dx=y/x. 02:56 Evaluate the integral: intxcos^3x^2sinx^2 dx 03:08 Evaluate the integral: intx^3 tan^4x^4sec^2x^4dx 03:44 Evaluate the integral:intdx/(7xsqrt((2x^4-4) 04:23 Perform the integration:intcos xcos 2 xcos3xdx 07...
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