UC Davis: #8 integrate ∫cos(5x)/(3+sin(5x)) dx

UT Austin: trig sq root integral ∫1/(sin(x) + cos(x)) dxsin(√x)/√(x cos^3(√x)) dx

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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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1st way: Differentiate the function w.r.t x log10(x)+logx(10)+logx(x)+log10(10)

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2 ways: derivative Find dy/dx, where tan(x+y)+tan(x-y)=1

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1st/2 ways: Find dy/dx of sin(x) + cos(y) =e^x

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2nd/2 ways: Find dy/dx of sin(x) + cos(y) =e^x

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2nd way: trig inverse ∫(2012)^x (2012)^ arc (sin(2012)^x)√(1-(2012)^2x) dx

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Find the power set of X if a) X= {a,b} b) X={a,b,c}

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trig integral ∫sec^7(x) tan^5(x) dx

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2nd example: Find the sum -0.31, -0.19, -0.07, 0.05, 0.17, 0.29 via median

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2nd way: If y=(ax-b)/(a-bx), prove that 2y1y3=3(y2)^2

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trig integral ∫sin^3(x)/cos^4(x) dx

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integral Find ∫1/(9-4x^2) dx

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exp Differentiate (i) b^e^x (ii) b^x&e (iii) (b^e)^x (iv) (b^x)^e

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2nd way: exp integral e^3x/(e^x +2) dx withOUT u-sub

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Alternate way: derivative If y=e^(a arc sin(x)), prove that (1-x^2)y2-xy1=a^2y

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