Indefinite Integrals

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Find the Integral of Nested Functions

Sometimes you need to integrate a function that is the composition of two functions — for example, the function 2x nested inside a sine function. If you were differentiating, you could use the Chain Rule [more…]

Integrate a Function Using the Sine Case

When the function you’re integrating includes a term of the form (a2bx2)n, draw your trig substitution triangle for the sine case. For example, suppose that you want to evaluate the following integral [more…]

Integrate a Function Using the Tangent Case

When the function you’re integrating includes a term of the form (a2 + x2)n, draw your trigonometry substitution triangle for the tangent case. For example, suppose that you want to evaluate the following [more…]

Setting Up Partial Fractions When You Have Distinct Factors

Your first step in any problem that involves partial fractions is to recognize which case you’re dealing with so that you can solve the problem. One case where you can use partial fractions is when the [more…]

Setting Up Partial Fractions When You Have Repeated Linear Factors

Your first step in any problem that involves partial fractions is to recognize which case you’re dealing with so that you can solve the problem. One case where you can use partial fractions is with repeated [more…]

Integrating Powers of Cotangents and Cosecants

You can integrate powers of cotangents and cosecants similar to the way you do tangents and secant. For example, here’s how to integrate cot8 x csc6 x: [more…]

Setting Up Partial Fractions When You Have Repeated Quadratic Factors

Your first step in any problem that involves partial fractions is to recognize which case you’re dealing with so that you can solve the problem. One case where you can use partial fractions is with repeated [more…]

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