#16 MIT 2022 Integration Bee Qualifying Exam

Review Add Math: Show a^m a^n = a^(m+n) where m & n are any 2 positive integers

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integral ∫ x dx withOUT using Power rule.

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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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2nd way: integral ∫ log √x(x^n) dx

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trig Write each expression as an equivalent algebraic expression involving only x.

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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx

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2nd way: STPM Math 2 Sem.2 Ex 11.4 Find the first 4 terms in the Maclaurin series of each of ...

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3rd/3 ways: Alternate way: Given 2 points, find equation of st line passing the ..

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4th/4parts: Maclaurin Series [ahp kia]

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STPM Math T Sem2: Find the Maclaurin series for xe^(-x) [ahp kia]

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2 ways: integral (3+5x)/(x(x-1)) dx

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2nd/3 parts: Growing patterns

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3rd/3ways: derivative (x+1)^(1/2) (x+2)^(1/3) (x+3)^(1/4) (x+4)^(1/5) (x+5)^(1/6)

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1st/parts: Derivative of the inverse circular functions

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2nd/3ways: Laplace Show that ...

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3rd/3 ways: Express (4x-17)/((x+4)(2x-3)) in partial fractions via withOUT cover rule

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2nd part: n^2 = (tn - tn-1)^2 where tn = nth triangular number

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integral ∫√(x-a)/x dx

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