MA 1723 - General Antiderivatives and Hyperbolic Functions and Inverse Funcitons

Function: x^{n}

General Antiderivative: \frac{x^{n+1}}{n+1}+C,n\ne-1

Function: \sin\left(kx\right)

General Antiderivative: -\frac{1}{k}\cos\left(kx\right)+C

Function: \cos\left(kx\right)

General Antiderivative: \frac{1}{k}\sin\left(kx\right)+C

Function: \sec^2(kx)

General Antid \frac{1}{k}\tan(kx)+C

Function: \csc^2(kx)

General Antiderivative: -\frac{1}{k}\cot(kx)+C

Function: \sec(kx)\tan(kx)

General Antiderivative: \frac{1}{k}\sec(kx)+C

Function: \csc(kx)\cot(kx)

General Antiderivative: -\frac{1}{k}\csc(kx)+C

Function: e^{kx}

General Antiderivative: \frac{1}{k}e^{kx}+C

Function: \frac{1}{x}

General Antiderivative: \ln\left\vert x\right\vert+C

Function: \frac{1}{\sqrt{1-k^2x^2}}

General Antiderivative: \frac{1}{k}\arcsin(kx)+C

Function: \frac{1}{1+k^2x²}

General Antiderivative: \frac{1}{k}\arctan(kx)+C

Function: \frac{1}{x\sqrt{k^2x^2-1}}

General Antiderivative: \operatorname{arcsec}(kx)+C

Function: a^{kx}

General Antiderivative: \frac{a^{kx}}{k\ln a}+C

e^^bln(a)

a^^b

Function: sinh(x)

Derivative: cosh(x)

Function: cosh(x)

Derivative: sinh(x)

Function: tanh(x)

Derivative: sech^²(x)

Function: sech(x)

Derivative: -sech(x)tanh(x)

Function: coth(x)

Derivative: -csch^²(x)

Function: csch(x)

Derivative: -csch(x)coth(x)

Function: sinh^^-1(x)

Derivative: 1/(1+x^²)^(^1/2)

Function: cosh^^-1(x)

Derivative: 1/(-1+x^²)^(^1/2)

Function: tanh^^-1(x)

Derivative: 1/(1-x^²)

Function: sech^^-1(x)

Derivative: -1/(x*(1-x2)^(1/2))

Function: coth^^-1(x)

Derivative: 1/(-x^²+1)

Function: csch^^-1(x)

Derivative: -1/(|x|*(1+x^²)^(^1/2))