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Anti-Derivative Rules

Exercises

Key Skills

Anti-Derivative Rules - Exercises | IB Math AAHL | Perplex

Anti-Derivative Rules

Anti-Derivative Rules

Antiderivatives of polynomials, trigonometric, inverse trigonometric, exponential, and logarithmic functions

Want a deeper conceptual understanding? Try our interactive lesson! (Plus Only)

Exercises

No exercises available for this concept.

Practice exam-style anti-derivative rules problems

Key Skills

Anti-Derivative of xⁿ, n∈ℚ

SL 5.6

∫xndx=n+1xn+1+C,n=−1📖

Anti-Derivative of sin and cos

SL 5.6

The integrals of sin and cos are

∫sinxdx ∫cosxdx=−cosx+C📖 =sinx+C📖

Anti-Derivative leading to tan

AHL 5.15

∫sec2xdx=tanx+C

Anti-Derivative leading to sec, cosec, and cot

AHL 5.15

∫secxtanxdx−∫cosecxcotx−∫cosec2x=secx+Cdx=cosecx+Cdx=cotx+C

Anti-Derivatives leading to arccos, arcsin, or arctan

AHL 5.15

∫√a2−x2−1dx=arccos(ax)+C📖

∫√a2−x21dx=arcsin(ax)+C📖

∫a2+x21dx=a1arctan(ax)+C📖

Anti-Derivative of e^x

SL 5.6

∫exdx=ex+C📖

Anti-Derivative of 1/x

SL 5.6

∫x1dx=ln∣x∣+C📖

Anti-Derivative of aˣ

AHL 5.15

∫axdx=lna1ax+C📖