trig Show (sec(x)+1)/sec^2(x) = sin^2(x)/(sec(x)-1)

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Swinburne U 2nd way: e^(-e^x) e^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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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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2 way: exp integral e^(ax+b)/1+e^(ax+b)) dx

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2nd way: integral sec^2(x) csc^2(x) dx

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log 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫ln(ln(x))/x dx

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IIT-1995 2nd way integral ∫x^5/(1+x^3) dx

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Gurjat CET-2007 2nd way log exp ∫e^(xln(2006) e^x dx

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Alternate way exp derivative (logf(x)(g(x)))^a

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prob stat It is known that P(X)=1/2 & P(Y)=1/4. Given that X & Y are mutually exclusive, find

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2 ways: 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫3x/((x-2)(x+1)) dx

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JHU: sq root integral ∫e^√x dx

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2nd way: integral 1/(1+tan(x)) dx

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2 ways: ∫ 1/(10x^2 -x-21) dx

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JHU: log ∫ln(t)/t^2 dt

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3rd/3ways: trig integral ∫sec(x) dx

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1st way: integral ∫x^k ln(x) dx = x^(k+1)/(k+1) ln(x) - x^(k+1)/(k+1)^2 + C where C ≠ -1

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1)integral ∫ x dx 2)integral ∫ ln(x)/x dx via inspection [NO u-sub]

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