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2nd way: integral ∫x^k ln(x) dx = x^(k+1)/(k+1) ln(x) - x^(k+1)/(k+1)^2 + C where C ≠ -1
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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2nd way: integral ∫ log √x(x^n) dx
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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
1st way: exp ∫(e^x)/x (1+x log(x)) dx
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trig Write each expression as an equivalent algebraic expression involving only x.
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3 ways: trig integral ∫sin([118]) cos([118]) d[118]
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2 ways: Find ∫(ax^x+bx+c) dx
AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(x)) dx
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prob & stat: Show ...
trig Prove each identity ... 1) to 10)
Suppose f & g are positive functions. Obtain the product rule for (fg)' by differentiating ...
4 ways: exp integral ∫a^(bx+c) dx
2nd part/3parts: Mean of -11,-2,7,...,70 SAME as Mean -11 & 70
rational function integrate ∫x^2/(x^6+a^6) dx
A function f is called even if f(-x)=f(x) for ALL x in the domain of f &
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trig integral ∫1/(√sin(x) √cos^7(x)) dx
2 ways: trig integral ∫ sec^2(x) csc^2(x) dx
2nd way: Express (4x-17)/((x+4)(2x-3)) in partial fractions via
Common log mistake: logb(xy^n) ≠ nlogb(xy)