Title: InkMaths / Integration: standard results
On every note of this deck, unless a note says otherwise:
Footer: Continue on inkmaths.co.uk · © 2026 InkMaths. All rights reserved.

Front: CHECK YOURSELF
Find the integral of 6e^(3x) with respect to x.
Back: 2e^(3x) + c: divide by the 3 from the chain rule, and never forget the constant on an indefinite integral.

Front: STANDARD RESULT — LEARN IT
Sine (x in radians):
∫ sin x dx = ?
Back: ∫ sin x dx = −cos x + c

Front: STANDARD RESULT — LEARN IT
Exponential:
∫ e^kx dx = ?
Back: ∫ e^kx dx = 1ke^kx + c

Front: STANDARD RESULT — LEARN IT
The n = −1 case:
∫ 1x dx = ?
Back: ∫ 1x dx = ln|x| + c

Front: STANDARD RESULT — LEARN IT
Cosine (x in radians):
∫ cos x dx = ?
Back: ∫ cos x dx = sin x + c

Front: SPOT THE ERROR
Say what is wrong with this claim:
The integral of sin x is cos x.
Back: It is −cos x + c. Check by differentiating your answer: the derivative of −cos x is sin x, which recovers the integrand. Differentiate-to-check catches every sign slip of this kind.

Front: STANDARD RESULT — LEARN IT
Power rule (n ≠ −1):
∫ x^n dx = ?
Back: ∫ x^n dx = x^n+1n+1 + c