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Integrals
20 cards·by Simiankolya
⌠e^(5-4x)dx
-1/4e^(5-4x) + C
⌠sin(πz)dz
-1/πcos(πz) + C
⌠cos^2(3Θ)dΘ
Θ/2 + 1/12sin(6Θ) + C
⌠xe(-2x)dx
(-x/2 - 1/4)e^(-2x) + C
⌠t^3 lnt dt
1/4t^4 lnt - 1/16t^4 + C
⌠4x/√(9-4x^2) dx
-√(9-4x^2) + C
⌠dx/√(9-4x^2)
1/2sin^-1(2x/3) + C
⌠(e^t - e^-t)/(e^t + e^-t) dt
ln(e^t + e^-t) + C
⌠cosα/(1 + sin^2α) dα
tan^-1(sinα) + C
⌠x/(1+x^4) dx
1/2(tan^-1(x/2)) + C
⌠xtan^-1(x) dx
1/2(x^2 + 1)tan^-1(x - 1/2x) + C
⌠sin^3(φ) dφ
1/3cos^3(φ) - cos(φ) + C
⌠sec^4(t) dt
1/3tan^3(x) + tan(x) + C
⌠(tan(√z))/(√z) dz
2ln | sec(√z) | + C
⌠5^2x dx
(5^2x)/2ln5 + C
⌠e^3x(sec(e^3x) dx
1/3ln | sec(e^3x) + tan (e^3x) | + C
⌠1/(1+√x) dx
2√x - 2ln(1+√x) + C
⌠y(2-y)^(3/2) dy
-2/5y(2-y)^(5/2) - 4/35(2-y)^(7/2) + C
⌠e^3x(sin(2x)) dx
3/13e^3x(sin(2x)) - 2/13e^3x(cos(2x)) + C
⌠(t^2 + 4t + 3)/(t+1) dt
1/2t^2 + 3t + C