How to Use Tangent Substitution to Integrate
With the trigonometric substitution method, you can do integrals containing radicals of the following forms: [more…]
How to Use Sine Substitution to Integrate
With the trigonometric substitution method, you can do integrals containing radicals of certain forms because they match up with trigonometric functions. A sine can take the place of a radical in a particular [more…]
How to Integrate Sine/Cosine Problems with an Odd, Positive Power of Cosine
When you integrate a trig integral that includes cosine, and if the power of cosine is odd and positive, you can convert and then use substitution to integrate. To make this conversion, you need to know [more…]
How to Integrate Tangent/Secant Problems with an Odd, Positive Power of Tangent
Here’s how you integrate a trig integral that contains tangents and secants where the tangent power is odd and positive. You’ll need the tangent-secant version of the Pythagorean identity: [more…]
How to Integrate Tangent/Secant Problems with an Even, Positive Power of Secant
Here’s how you integrate a trig integral that contains tangents and secants where the secant power is even and positive. Like with all tangent/secant integrals, you use the tangent-secant version of the [more…]
How to Integrate Problems with an Even, Positive Power of Tangent
Here’s how you integrate a trig integral that contains tangents (and no secant factors) where the tangent power is even and positive. [more…]
How to Use Trig Substitution to Integrate
With the trigonometric substitution method, you can do integrals containing radicals of the following forms (given a is a constant and u is an expression containing [more…]
How to Integrate Sine/Cosine Problems with an Odd, Positive Power of Sine
Here’s how you integrate a trig integral that contains sines and cosines where the power of sine is odd and positive. You lop off one sine factor and put it to the right of the rest of the expression, [more…]
How to Integrate Sine/Cosine Problems with Even, Nonnegative Powers of Both Sine and Cosine
Here’s how you integrate a trig integral that contains sines and cosines where the powers of both sine and cosine are even and nonnegative (in other words, zero or positive). You first convert the integrand [more…]
How to Solve Integrals with Variable Substitution
In Calculus, you can use variable substitution to evaluate a complex integral. Variable substitution allows you to integrate when the Sum Rule, Constant Multiple Rule, and Power Rule don’t work. [more…]
How to Use Trig Substitution to Integrate radicals of the sine form
Before reading this article, you should check out the discussion of trig substitution in the companion article, “How to Use Trig Substitution to Integrate.” [more…]
