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derivative (f(x)/g(x))^h(x)
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2nd way: integral ∫ log √x(x^n) dx
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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(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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Evaluate the integrals
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
2 ways: Find ∫(ax^x+bx+c) dx
Suppose f & g are positive functions. Obtain the product rule for (fg)' by differentiating ...
exp Differentiate (i) b^e^x (ii) b^x&e (iii) (b^e)^x (iv) (b^x)^e
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Common log mistake: logb(xy^n) ≠ nlogb(xy)
A function f is called even if f(-x)=f(x) for ALL x in the domain of f &
trig Prove each identity ... 1) to 10)
Show log b^n(x^m) = m/n logb(x)
2nd way: Express (4x-17)/((x+4)(2x-3)) in partial fractions via