Calculus: Find nth derivative of log(ax+b)

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Let f(x) be a polynomial of degree 1. If f(10)-f(5)=15, then f(20)-f(5)=?

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Let f(x) be a polynomial of degree 1. If f(10)-f(5)=15, then f(20)-f(5)=?

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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alternate way: count sum 1 + 2 + 3+... + n via "polynomial"

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alternate way: count sum 1 + 2 + 3+... + n via "polynomial"

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

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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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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(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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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx

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2nd way: integral ∫ log √x(x^n) dx

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