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1st way: exp ∫(e^x)/x (1+x log(x)) dx
18 Views
MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx
15 Views
#lyndo
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Logical equivalent involving ... tautology & contradiction
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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
25 Views
Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
Solve the following differential equation cos^2(x)dy/dx +y = tan(x)
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2nd/3ways: trig integral ∫sec(x) dx
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2nd way: integral ∫ log √x(x^n) dx
60 Views
MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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2nd/2ways: count perm Show P(n,2)+P(n,1)=n^2
Derivative: Don't blindly use the Quotient Rule every time you see a quotient
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If y=acos(ln(x)) + bsin(ln(x)), show that x^2y2 + xy1 +y=0
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Vandermonde's Identity
Florida International U: Find derivatives ...defined implicitly ... (a)-(c)
2 ways: trig integral ∫cos^2(x) dx
4 Views
3 ways: trig integral 1/(1+cos(x)) dx
1 View
Integrate ∫x^3 sin(arc tan(x^4))/(1+x^8) dx