#16 MIT 2022 Integration Bee Qualifying Exam

Seihantai na Kimi to Boku Episode 1

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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx

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2nd way: derivative (x^x)^x

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

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2nd part: STPM Math T Sem.2: 12.1 Numerical solution of Equations

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Mohammad Ali Jinnah University: Integrate the followings.

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Show log b^n(x^m) = m/n logb(x)

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2nd/2parts: Linear interpolation (2 given points)

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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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1st way: Differentiate the function w.r.t x log10(x)+logx(10)+logx(x)+log10(10)

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Tensei shitara Dragon no Tamago datta Episode 2

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exp integral ∫a^(√√x^3)/√√x dx

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Alternate way: trig integral ∫sin(x) dx

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trig integral cos^2(x) sin(x) dx

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2 ways: sq root √x^x

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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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3 ways: trig Show sec(2x)=sec^2(x)/(2-sec^2(x))

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Calculus: If u=f(x+cy)+g(x-cy) then uxx / uyy ?

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