Antiderivative of ln x: x ln x − x + C, Step by Step
The antiderivative of ln x is x ln x − x + C. See the integration by parts trick, a quick check, and the integrals of ln(2x), (ln x)², ln x/x and log x.
Prof. Adrian Cole
Antiderivative of sin x: Answer, Proof and Examples
The antiderivative of sin x is −cos x + C. See why the minus sign appears, a memory trick, the antiderivative of cos x, and sin 2x, sin²x and x sin x.
Best Free Antiderivative Calculators Compared (With a 5-Problem Test)
Compare Wolfram|Alpha, Symbolab, Integral-Calculator.com, GeoGebra, Desmos and more, then test any tool yourself with 5 integrals.
How to Check an Antiderivative: 4 Easy Methods
Check any antiderivative in seconds: differentiate it, plug in numbers, compare different-looking answers, or read the graph. Worked examples included.
Can a Calculator Do Integrals? Which Ones Can Find Antiderivatives
Which calculators can find antiderivatives? Compare TI-84, TI-89, TI-Nspire CAS, HP Prime and online tools, and see which integrals no calculator can do.
Should Students Use Antiderivative Calculators? Pros, Cons and Rules
Why do students use antiderivative calculators, and is it cheating? See the benefits, the risks, and 5 rules for learning with a calculator.
How to Use an Antiderivative Calculator: A Step-by-Step Tutorial
Learn to use an antiderivative calculator: how to type functions, read the answer and steps, check the result, and fix the most common input errors.
Antiderivative of Exponential Functions: a^x, 2^x, 10^x and More
The antiderivative of a^x is a^x/ln a + C. See where ln a comes from, work through 2^x, 10^x, (1/2)^x and a^(kx), and solve a real growth problem.
Antiderivatives of Trig Functions: sin, cos, tan, sec, csc, cot
Antiderivatives of all six trig functions, sin, cos, tan, cot, sec and csc, with a short proof for each, plus sec², sin², tan² and worked examples.
Integration by Parts: Formula, LIATE Rule and 8 Examples
Learn the integration by parts formula, how to choose u with LIATE, the tabular method, and 8 worked examples with answers you can check.