CAIE IGCSE Additional Math 14.12 integrate composite functions

Use this composite-integration page to adjust for inner derivatives, evaluate exact limits and use conditions to complete y or dy/dx.

Exam points

Integrate composite forms such as e^(2x), ln-related terms or trig functions.
Adjust constants for inner derivatives when integrating expressions like sin(ax+b).
Use initial conditions or limits to complete expressions for y, dy/dx or a definite value.

[Maximum number: 3]

Find $\int\left(\frac{1}{(2x-6)^3}+\cos x\right)\,dx$ .

$\frac{(2x-6)^{-2}}{-2\times2}+\sin x(+c)$
oe, isw
B1 for $\sin x$
B2 for $\frac{(2x-6)^{-2}}{-2\times2}$
or B1 for $\frac{(2x-6)^{-2}}{-2}$ soi

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