Integral of sec 3x

Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int sec 3x cot 3x dx, integral of sec 3x. First, we must identify a section within the integral with a new variable let's call it uwhich when substituted makes the integral easier. We see that 3x it's a good candidate for substitution.

The integral of secant cubed is a frequent and challenging [1] indefinite integral of elementary calculus :. This antiderivative may be found by integration by parts , as follows: [2]. This admits a decomposition by partial fractions :. Just as the integration by parts above reduced the integral of secant cubed to the integral of secant to the first power, so a similar process reduces the integral of higher odd powers of secant to lower ones. This is the secant reduction formula, which follows the syntax:.

Integral of sec 3x

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It can be calculated using the substitution method. Integration is the reverse process of differentiation, hence determining the integration of sec 3x is the same as finding the antiderivative of sec 3x. Further in this article, we will evaluate the integration of sec 3x step-wise using the substitution method. We will also find the integration of sec 3x combined with different functions and solve a few examples for a better understanding. The integration of sec 3x is the process of finding the antiderivative of sec 3x. We can calculate the integration of sec 3x using the substitution method by substituting 3x with another variable and solving the integral. Let now go through the formula for the integral of sec 3x. The image given below shows the integral of sec 3x formula:. We will prove this using the substitution method. We will use the derivative formulas of tan A and sec A which are:.

Integral of sec 3x

Integral of sec cube x along with its formula and proof with examples. In calculus , the integral is a fundamental concept that assigns numbers to functions to define displacement, area, volume, and all those functions that contain a combination of tiny elements. It is categorized into two parts, definite integral and indefinite integral.

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