Compute the inverse Laplace transform of a function for a symbolic parameter t:

Use a numerical value for the parameter:

TraditionalForm formatting:

Reciprocal of a linear function:

Reciprocal of a quadratic function:

Functions whose inverses are trigonometric functions:

Functions whose inverses are hyperbolic functions:

More examples of rational functions:

Function involving a square root:

Function involving exponential and square root functions:

Other algebraic functions:

Inverse Laplace transform leading to a Bessel function:

Inverse of an arctangent function:

Inverse Laplace transform of a logarithmic function:

Logarithm of a rational function:

Plot the result:

Product of a logarithm and a power function:

Function involving the square of a logarithm:

Function involving BesselK:

Ratio of an incomplete gamma function and a power function:

Inverse of a polygamma function:

Inverse of a function involving an error function:

Error function composed with a square root:

Inverse transforms of the LegendreP and LegendreQ functions:

Complex plots of the Legendre functions:

Product of BesselI and Exp:

ComplexPlot of the frequency-domain function:

Product of BesselJ and Gamma functions:

ComplexPlot of the frequency-domain function:

Composition of exponential integral and square root functions:

Product of two ParabolicCylinderD functions:

Inverse transforms involving elliptic integral functions:

Inverse transform of EllipticTheta:

The inverse of the following function is a piecewise function:

Plot the inverse:

Inverse of an exponential function leading to a box function:

Inverse of an exponential function leading to a piecewise trigonometric function:

Inverse leading to a staircase function:

More involved staircase function:

The inverse of the following function is periodic with respect to t:

Activate the sum:

Plot to verify that the result is a square wave:

Function whose inverse is the absolute value of the sine function:

Activate and plot the result:

Function whose inverse is a trapezoidal wave:

A more involved piecewise example:

Inverse of an exponential function is the Dirac function:

Inverse of the product of an exponential function and a power of s is a derivative of the Dirac function:

The inverse of the hyperbolic secant is a series of Dirac functions:

Hyperbolic cotangent:

Inverse Laplace transform of a bivariate rational function:

Verify the result:

Rational function that is separable with respect to p and q:

Rational function that is not separable with respect to p and q:

Rational function whose inverse is related to BesselJ:

Inverse Laplace transform of a bivariate function involving a radical:

Inverse Laplace transform of a multivariate function in three variables:

Rational function:

Function involving a logarithm:

Calculate the inverse Laplace transform at a single point:

Alternatively, calculate the inverse Laplace transform symbolically:

Then evaluate it for a specific value of t:

Plot the inverse Laplace transform numerically and compare it with the exact result:

Function whose inverse is a piecewise function with respect to t:

Function whose inverse is a periodic function with respect to t:

ComplexPlot of an algebraic function in the -domain:

Inverse Laplace transform of this algebraic function:

Laplace transform to the -domain:

Inverse Laplace transform of the algebraic function:

Plot in time domain:

Laplace transform to the -domain:

Inverse Laplace transform of the algebraic function involving parameters:

Laplace transform to the -domain:

By default, InverseLaplaceTransform assumes that the result is defined for non-negative t:

Use GenerateConditions to obtain the range of validity for the result:

Use the default method for numerical evaluation:

Use Method to obtain the result from different methods:

Use WorkingPrecision to obtain a result with arbitrary precision: