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Integrals

QuestionAnswer
∫u dv du uv + ∫ v du
∫1/x dx ln|x| +C
∫a^x dx a^x / (ln(a)) +C
∫sin(x) dx -cos(x) +C
∫cos(x) dx sin(x) +C
∫tan(x) dx ln|sec(x)| +C
∫cot(x) dx ln|sin(x)| +C
∫sec(x) dx ln|sec(x) + tan(x)| +C = ln|tan(u/2 + pi/4)| +C
∫csc(x) dx ln|tan(x/2)| +C = -ln|csc(x) + cot(x)| +C
∫sec^2(x) dx tan(x) +C
∫csc^2(x) dx -cot(x) +C
∫tan^2(x) dx tan(x)-x +C
∫cot^2(x) dx -cot(x)-x +C
∫sin^2(x) dx x/2-(sin^2(x)/4) + C
∫cos^2(x) dx ½(x + ¼sin(2x)) + C
∫sec(x)tan(x) dx sec(x) +C
∫csc(x)cot(x) dx -csc(x) +C
∫1/(x^2 + a^2) dx tan^-1(x/a)/a +C
∫1/(x^2 - a^2) dx ln((x-a)/(x+a))/2a +C
∫1/sqrt(a^2 - x^2) dx sin^-1(x/a) +C
∫1/sqrt(x^2 + a^2) dx ln(x + sqrt(x^2 + a^2)) +C
∫1/sqrt(x^2 - a^2) dx ln(x + sqrt(x^2 - a^2)) +C
∫1/(x sqrt(x^2 - a^2)) dx 1/(a sec|x/a|) +C
∫1/(x sqrt(x^2 + a^2)) dx -ln((a + sqrt(x^2 + a^2))/x)/a
∫1/(x sqrt(x^2 - a^2)) dx -ln((a + sqrt(x^2 - a^2))/x)/a
∫x e^x dx x e^x - e^x +C
∫e^x dx e^x +C
∫ln(x) dx x ln(x) - x + C
Created by: nstrombo
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