Substitution (Reverse Chain Rule) (AQA A-Level Mathematics): Quizzes

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Substitution (Reverse Chain Rule)
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What is the substitution method also known as?

Reverse Chain Rule

When choosing uu in substitution, what should it equal?

Inner function whose derivative is present

After integrating with respect to uu, what must you do?

Substitute uu back with xx expression

For f(ax+b)f(ax+b) form, what do you divide by?

Differential of the bracket

What is ∫f′(x)f(x)dx\int \frac{f'(x)}{f(x)} dx equal to?

ln⁡∣f(x)∣+c\ln |f(x)| + c

What is ∫f′(x)(f(x))ndx\int f'(x)(f(x))^n dx equal to?

1n+1(f(x))n+1+c\frac{1}{n+1}(f(x))^{n+1} + c

What is ∫tan⁡2x dx\int \tan^2 x \, dx equal to?

tan⁡x−x+c\tan x - x + c

When is substitution preferred over integration by parts?

When a differential relationship exists

What is the derivative of tan⁡kx\tan kx?

ksec⁡2kxk\sec^2 kx

What identity helps evaluate ∫cot⁡2x dx\int \cot^2 x \, dx?

cot⁡2x+1≡csc⁡2x\cot^2 x + 1 \equiv \csc^2 x

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