3 ways: trig integral ∫sin([118]) cos([118]) d[118]

COMMON MISTAKE: (1) logb(m) logb(n) ≠ logb(m+n)

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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

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2nd way: integral ∫ log √x(x^n) dx

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

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

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If 4xe^(xy)=y+5sin^2(x) then find the value of y'(0)

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integral ∫x^2/√(x^2+a^2) dx

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

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derivative differentiate x^sin(x) + (sin(x))^cos(x)

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Prove Σ1/((k-1)(k+1))=(3n^2-n-2)/(4n(n+1)) where k=2 to n ∀n ≥ 2

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exp integral e^x (f(x) + f'(x)) dx

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exp derivative (log f(ax+b) (g(cx+d)))^h(mx+n)

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2nd/2ways: r-Permutations

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3rd way: nCr = (n-1)Cr + (n-1)C(r-1)

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3rd/3ways: count comb A set with n elements has 2^n subsets

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2 ways: ∫x√(x+1) dx

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Always ZERO

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trig integral ∫sin(2x) cos(2x)/(9-cos^4(2x)) dx

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