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In the video, we work out the antiderivatives of the four remaining trig functions. Depending upon your instructor, you may be expected to memorize these antiderivatives. The antiderivatives of tangent and cotangent are easy to compute, but not so much secant and cosecant.
Free antiderivative calculator - solve integrals with all the steps. Type in any integral to get the solution, steps and graph.
Solve integration problems involving products and powers of sinx and cosx. Solve integration problems involving products and powers of tanx and secx. Use reduction formulas to solve trigonometric integrals. In this section we look at how to integrate a variety of products of trigonometric functions.
Functions involving trigonometric functions are useful as they are good at describing periodic behavior. This section describes several techniques for finding antiderivatives of certain combinations of trigonometric functions.
In this section we are going to look at quite a few integrals involving trig functions and some of the techniques we can use to help us evaluate them. Let’s start off with an integral that we should already be able to do. ∫cosxsin5xdx = ∫u5du using the substitution u = sinx = 1 6sin6x + c.
Compute the following integrals using the guidelines for integrating powers of trigonometric functions. Use a CAS to check the solutions. ( Note : Some of the problems may be done using techniques of integration learned previously.)
The following is a list of integrals (antiderivative functions) of trigonometric functions. For antiderivatives involving both exponential and trigonometric functions, see List of integrals of exponential functions. For a complete list of antiderivative functions, see Lists of integrals.
Recall the definitions of the trigonometric functions. The following indefinite integrals involve all of these well-known trigonometric functions. Some of the following trigonometry identities may be needed. It is assumed that you are familiar with the following rules of differentiation.
Calculus: How to find Antiderivatives, the formula for the antiderivatives of powers of x and the formulas for the derivatives and antiderivatives of trigonometric functions, antiderivatives and integral formulas, with video lessons, examples and step-by-step solutions.
You can verify this is the correct antiderivative by differentiating the result and comparing it to the original integrand. You may need to use some trig identities. Practice 3.