Practice question · Match the pairs
Match each integrand to its antiderivative.
- 1/x
- e^x
- cos x
- x^2
- sin x + C
- x^3/3 + C
- e^x + C
- ln|x| + C
Hints
- Three of these are reversed standard derivatives you already know.
- Only one of the four is handled by the power rule.
Show the answer
- 1/x → ln|x| + C
- e^x → e^x + C
- cos x → sin x + C
- x^2 → x^3/3 + C
Why
These four are the working vocabulary of the lesson. Note that is its own antiderivative, the only function (up to a factor) with that property, and that 1/x needs the absolute value, since ln is undefined for negative arguments.
Practise Antiderivatives and Indefinite Integrals
The app has 6 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.