Substitution (Reverse Chain Rule) (Edexcel 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

In substitution, what should uu typically equal?

Inner function with derivative present

What is ∫2x⋅ex2dx\int 2x \cdot e^{x^2} dx equal to?

ex2+Ce^{x^2} + C

For ∫f(ax+b)dx\int f(ax+b) dx, what do you divide by?

Derivative of the bracket

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

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⁡2xdx\int \tan^2 x dx equal to?

tan⁡x−x+c\tan x - x + c

What is the derivative of sec⁡x\sec x?

sec⁡xtan⁡x\sec x \tan x

When should substitution be used over by parts?

When differential relationship exists

Which method for ∫x2ex3+4dx\int x^2 e^{x^3 + 4} dx?

Substitution (reverse chain rule)

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