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

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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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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

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

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

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2nd way: integral ∫ log √x(x^n) dx

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1st/2ways: exp e^g(x) (g'(x)f(x) + f'(x)) dx

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2 ways: ∫ (1-x)/√(1-x^2) dx

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1st/2parts 3 ways: tn-1 + tn = n^2 where tn = nth triangular number

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

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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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2nd/2ways: Find lim (z^3-8)/(z-2) for z tends to 2

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2nd/2 parts: 2 (elementary) rules

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exp integral ∫(1+e^x)/(1-e^x) dx

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2nd/2 ways: FInd partial fractions (3x^2+9x-20)/(x^2+x-6)

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2nd way: trig integral ∫sin^6(ax+b) cos^6(ax+b) dx

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COMMON MISTAKE: derivative (x)' 1/2 x^(-1/2)

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