#4 2022 2nd/2 ways: MIT Integration Bee Qualifying Exam

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2nd way: integral ∫ log √x(x^n) dx

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2nd way: integral ∫ log √x(x^n) dx

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

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

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

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

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If x=at^2,, y=2at, then find d2y/dx2

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If x=at^2,, y=2at, then find d2y/dx2

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx

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

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

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

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

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Review Add Math: 1.2/parts: Show a^m a^n = a^(m+n) where m & n are any 2 positive integers

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Review Add Math: 1.2/parts: Show a^m a^n = a^(m+n) where m & n are any 2 positive integers

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2nd way: Express (4x-17)/((x+4)(2x-3)) in partial fractions via

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2nd way: Express (4x-17)/((x+4)(2x-3)) in partial fractions via

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#5 MIT 2022 Integration Bee Qualifying Exam

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#5 MIT 2022 Integration Bee Qualifying Exam

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3 ways: Derivative x^(-1/x)

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3 ways: Derivative x^(-1/x)

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inverse trig Derivative arc sin(x)

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inverse trig Derivative arc sin(x)

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2nd/2 parts: 2 (elementary) rules

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2nd/2 parts: 2 (elementary) rules

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Solve x(x-1)dy/dx - (x-2)y=x^3(2x-1) via Integrating Facto[IF]

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Solve x(x-1)dy/dx - (x-2)y=x^3(2x-1) via Integrating Facto[IF]

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sq root derivative √x [Good to know the result]

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sq root derivative √x [Good to know the result]

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4 ways: Evaluate Σ(2k+1) k=1,20

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4 ways: Evaluate Σ(2k+1) k=1,20

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exp Differentiate (i) b^e^x (ii) b^x&e (iii) (b^e)^x (iv) (b^x)^e

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exp Differentiate (i) b^e^x (ii) b^x&e (iii) (b^e)^x (iv) (b^x)^e

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#16 MIT 2022 Integration Bee Qualifying Exam

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#16 MIT 2022 Integration Bee Qualifying Exam

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trig Evaluate each expression below withOUT using a calculator.

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trig Evaluate each expression below withOUT using a calculator.

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