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2nd way: ∫cos(x)/√(sin^2(x)+4sin(x)+3) dx
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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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derivative If y=acos(log(x)) + bsin(log(x)), prove that x^2y2+xy1+y=0
1st/2 ways: MIT Integration Bee
Alternate way: derivative If y=e^(a arc sin(x)), prove that (1-x^2)y2-xy1=a^2y
3 ways: exp integral ∫ln(e^x) + ln(e^(-x)) dx
2nd way: log sqr integral ∫ln(x)/x dx
derivative If y=(a+bx)e^(-nx), prove that y2+2ny1+n^2y=0
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2nd way: integral ∫ 1/(1+x+x^2) dx
#6 2024 MIT Integration Bee Qualifying Exam
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2nd way: trig integral (sin(x)-cos(x))^2 dx
2nd way: sq rt integral ∫(√x)/(x+1) dx
2nd way: sq rt integral ∫ √√e^x dx
Lamar U: #11 trig integral ∫csc^6(x/4) cot^4(x/4) dx
derivative Find d2y/dx2 for this function y=ln(x)/(1-x)
2nd way: trig integral (3-tan^2(x))/(cot(x)-3tan(x)) dx
2nd way: trig derivative tan(arc tan(x))