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Show ∫ f'(x)/√f(x) dx = 2 √f(x) + C
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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)
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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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Pantun Melayu [Pulau Pandan Jauh Ke Tengah]
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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx
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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx
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2nd way: derivative (x^x)^x
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exp integral e^x (f(x) + f'(x)) dx
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Alternate way: ∫(5+2x)/(x+x^4)dx
2nd way: integral ∫e^(x/2)/(1+e^x) dx
JEE Main integral ∫x^5 /√(1+x^3) dx
1st/2parts: Linear interpolation (2 given points)
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2nd way: sq rt integral ∫(√x)/(x+1) dx
2 ways: trig integral ∫csc^2(x)/sec(x) dx
alternate way: count sum 1 + 2 + 3+... + n via "polynomial"
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prob stat: A group consists of 4 girls & 7 boys. In how many ways can a team of 5 members ...
2nd/2 ways: FInd partial fractions (3x^2+9x-20)/(x^2+x-6)
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9Screen Recording 2023-12-02 at 2.43.56 AM
1st/2ways: permutation Show P(n,2)+P(n,1)=n^2
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2nd/2ways: trig Evaluate (sin^6(x) + cos^6(x))/(sin^2(x) cos^2(x)) dx