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#8 Lamar U: evaluate integral sec^8(t/2) tan^5(t/2) dt
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)
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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx
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Review: Linear form, Quadratic form & Bilinear form
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2 ways: sq root derivative 1/(√√(1/√x))
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2nd/3ways: trig integral ∫sec(x) dx
integral ∫ x dx withOUT using Power rule.
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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trig Write each expression as an equivalent algebraic expression involving only x.
prob stat In a sample of n= 6 scores, 5 of the scores are each above the mean by one point.
2nd way: sq rt integral ∫(√x)/(x+1) dx
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3rd/3ways: trig integral ∫sec(x) dx
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A function f is called even if f(-x)=f(x) for ALL x in the domain of f &
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4th way: rational function integral ∫x^3/√ (1+x^2) dx
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3rd way: rational function integral ∫x^3/√ (1+x^2) dx
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Compute the derivatives of the following function
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Alternate way: integral ∫ax+b dx
commutative: ab=ba via "picture"
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