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Penn. State U: Suppose the p.m.f of discrete random variable X is ...
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2nd/3ways: trig integral ∫sec(x) dx
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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx
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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx
MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx
MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx
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2nd way: integral ∫ log √x(x^n) dx
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Derivative: Don't blindly use the Quotient Rule every time you see a quotient
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2nd/2ways: Taylor series of sin(x) [Maclaurin's series]
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trig integral sin(tan(x)) cos(tan(x)) sec^2(x) dx [chain rule in reverse]
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trig integral ∫sin(x) cos(x) cos(2x) cos(4x) cos(8x) cos(16x) cos(32x) dx
log sq root integral ∫ln(√ x^3)/√ √ x dx
2nd way: 1) ∫1/(a + √b x^2) dx vs 2) ∫1/(a + √b x^2) dx
Is 4cos^3(x)-3cos(x) EVEN, ODD, NEITHER, BOTH EVEN & ODD?
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Compute the derivatives of the following function
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Find nth derivative of e^(ax)
1st/2ways: Taylor series of cos(x)
2 ways: derivative a^f(g(x))