Memorize Calc Final

∫arcsin(x) dx

xarcsin(x)+√(1−x²)+C

∫arccos(x) dx

xarccos(x)−√(1−x²)+C

∫arctan(x) dx

xarctan(x)−(1/2)ln(1+x²)+C

∫arccot(x) dx

xarccot(x)+(1/2)ln(1+x²)+C

∫arcsec(x) dx

xarcsec(x)−ln(|x|+√(x²−1))+C

∫arccsc(x) dx

xarccsc(x)+ln(|x|+√(x²−1))+C

∫a^x dx

a^x/ln(a)+C

∫e^x dx

e^x+C

∫ln(x) dx

xln(x)−x+C

∫sin(x) dx

−cos(x)+C

∫cos(x) dx

sin(x)+C

∫sec²(x) dx

tan(x)+C

∫csc²(x) dx

−cot(x)+C

∫sec(x)tan(x) dx

sec(x)+C

∫csc(x)cot(x) dx

−csc(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

∫csc(x) dx

ln|csc(x)−cot(x)|+C

∫dx/(1+x²)

arctan(x)+C

∫dx/√(1−x²)

arcsin(x)+C

∫dx/(x²+a²)

(1/a)arctan(x/a)+C

∫dx/√(a²−x²)

arcsin(x/a)+C

e^x Maclaurin Series

Σ(x^n/n!) from n=0 to ∞ = 1+x+x²/2!+x³/3!+…

sin(x) Maclaurin Series

Σ((-1)^n x^(2n+1)/(2n+1)!) from n=0 to ∞ = x−x³/3!+x⁵/5!−…

cos(x) Maclaurin Series

Σ((-1)^n x^(2n)/(2n)!) from n=0 to ∞ = 1−x²/2!+x⁴/4!−…

1/(1−x) Maclaurin Series

Σx^n from n=0 to ∞ = 1+x+x²+x³+… for |x|<1

1/(1+x) Maclaurin Series

Σ((-1)^n x^n) from n=0 to ∞ = 1−x+x²−x³+… for |x|<1

ln(1+x) Maclaurin Series

Σ((-1)^(n+1)x^n/n) from n=1 to ∞ = x−x²/2+x³/3−x⁴/4+… for −1<x≤1

ln(1−x) Maclaurin Series

−Σ(x^n/n) from n=1 to ∞ = −x−x²/2−x³/3−… for |x|<1

arctan(x) Maclaurin Series

Σ((-1)^n x^(2n+1)/(2n+1)) from n=0 to ∞ = x−x³/3+x⁵/5−… for |x|≤1

sin(x) Maclaurin Series

Σ(x^(2n+1)/(2n+1)!) from n=0 to ∞ = x+x³/3!+x⁵/5!+…

cos(x) Maclaurin Series

Σ(x^(2n)/(2n)!) from n=0 to ∞ = 1+x²/2!+x⁴/4!+…

(1+x)^p Binomial Series

Σ[(p(p−1)…(p−n+1)/n!)x^n] from n=0 to ∞ = 1+px+p(p−1)x²/2!+… for |x|<1

1/√(1−x²) Maclaurin Series

1+(1/2)x²+(3/8)x⁴+(5/16)x⁶+…

arcsin(x) Maclaurin Series

x+x³/6+3x⁵/40+5x⁷/112+… for |x|≤