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3 ways: trig Show sec(2x)=sec^2(x)/(2-sec^2(x))
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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 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: integral ∫ log √x(x^n) dx
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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
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3rd/3 ways: Alternate way: Given 2 points, find equation of st line passing the ..
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2 ways: exp integral ∫(p^x + q^x)/r^x dx
derivative log f(g(x)) (p(r(x)))
examples 2x2 matrix withOUT an inverse
1st/2 ways: derivative y=(ln(x))^x
2 ways: derivative a^f(g(x))
exp Differentiate (i) b^e^x (ii) b^x&e (iii) (b^e)^x (iv) (b^x)^e
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2nd way: trig integral ∫1/(1+sin^2(x))cos^2(x))
trig integral ∫cos(x) sin(x)/(cos^2(x)-1) dx
2nd way: trig inverse ∫(2012)^x (2012)^ arc (sin(2012)^x)√(1-(2012)^2x) dx
2nd way: integral ∫x^k ln(x) dx = x^(k+1)/(k+1) ln(x) - x^(k+1)/(k+1)^2 + C where C ≠ -1
Show log b^n(x^m) = m/n logb(x)
2 ways: trig integral ∫ sec^2(x) csc^2(x) dx
logic: If p then q ...