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Alternate way: Evaluate exp integral ∫1/√(1-e^(2x)) dx
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx
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2nd way: integral ∫ log √x(x^n) dx
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log sq root integral ∫ln(√ x^3)/√ √ x dx
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Find the derivative of f(x)=(1+2x^2)(x-x^2) in 2 ways
2nd/10parts: Logical complement
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UT Austin: integral ∫(1+sin^(x-1)) sin(x-1) cos(x-1) dx
"baby" fact: exp e^(ix)
2 ways: trig exp derivative e^(sin(x)) sin(e^x)
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UC Davis #16: Prove (fgh)'=f'gh+fg'h+fgh' [differentiation using the product rule]
trig integral cos(a√x +b) dx
Find the number of subsets {1,{2,3}}
OSU Math 1151 Practice3: Compute the derivative.
2nd way: 1) ∫1/(a + √b x^2) dx vs 2) ∫1/(a + √b x^2) dx
Example: Find the sum
There are 2 lines. One line has 3 points & the other line has 6 points.
Alternate way: integral ∫ax+b dx
2nd/3 ways: How many chords can be drawn through 21 points on a circle?
2nd way: trig integral ∫√tan(x)/(sin(x) cos(x)) dx