Integrate x^2 sqrt(x+1) dx

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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(x)) dx

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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^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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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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logic: tautology (¬p→q)∧(¬p→¬q) →p

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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"

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Solve the differential equation cos^2(y) dx +(1+e^(-x) sin(y) dy=0

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log sq root integral ∫ln(√ x^3)/√ √ x dx

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2 ways: trig integral ∫cos^2(x) dx

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2nd/3ways: exp Derivative x^x

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Alternate way: trig integral ∫sin(x) dx

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Alternate way: trig integral ∫cos(x) dx

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