Find the derivative of f(x)=(1+2x^2)(x-x^2) in 2 ways

Lamar U: trig integral ∫cos^5(2t) sin^2(2t) dt

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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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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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3 ways: sum Show 1+3+5+...nth term = n^2

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1st/3 ways: Show 1+2+3+...+n=n(1+n)/2 via picture

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Find the number of different 8 letter arrangements that can be made from the letters of the word ..

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integral ∫e^x(1/x - 1/x^2) dx

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5th/10parts: Material implication

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3rd/10parts: Exclusive disjunction

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UC Davis: 4 ways exp integral ∫7^(2x+3) dx

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The sum of 3 numbers in AP is 15 & the sum of their squares is 3. Find the numbers.

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2 ways: ∫x√(x+1) dx

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2 ways: exp integral ∫(p^x + q^x)/r^x dx

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sum Show 1+3+5+...+nth term = n^2 via picture

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3 ways: trig integral ∫tan(x) sec^2(x) dx

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2nd/2ways: Evaluate trig integral ∫1/(sin(x) + cos(x)) dx

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integral ∫(x^2-x+1)/(x^2+x+1) dx

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