# Laplace Transform Calculator

The calculator will find the Laplace Transform of the given function.

Recall, that the Laplace transform of a function is $$F(s)=L(f(t))=\int_0^{\infty} e^{-st}f(t)dt$$$. Usually, to find the Laplace Transform of a function, one uses partial fraction decomposition (if needed) and then consults the table of Laplace Transforms. • In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. • In general, you can skip parentheses, but be very careful: e^3x is e^3x, and e^(3x) is e^(3x). • Also, be careful when you write fractions: 1/x^2 ln(x) is 1/x^2 ln(x), and 1/(x^2 ln(x)) is 1/(x^2 ln(x)). • If you skip parentheses or a multiplication sign, type at least a whitespace, i.e. write sin x (or even better sin(x)) instead of sinx. • Sometimes I see expressions like tan^2xsec^3x: this will be parsed as tan^(2*3)(x sec(x)). To get tan^2(x)sec^3(x), use parentheses: tan^2(x)sec^3(x). • Similarly, tanxsec^3x will be parsed as tan(xsec^3(x)). To get tan(x)sec^3(x), use parentheses: tan(x)sec^3(x). • From the table below, you can notice that sech is not supported, but you can still enter it using the identity sech(x)=1/cosh(x). • If you get an error, double check your expression, add parentheses and multiplication signs where needed, and consult the table below. • All suggestions and improvements are welcome. Please leave them in comments. The following table contains the supported operations and functions:  Type Get Constants e e pi pi i i (imaginary unit) Operations a+b a+b a-b a-b a*b a*b a^b, a**b a^b sqrt(x), x^(1/2) sqrt(x) cbrt(x), x^(1/3) root(3)(x) root(x,n), x^(1/n) root(n)(x) x^(a/b) x^(a/b) abs(x) |x| Functions e^x e^x ln(x), log(x) ln(x) ln(x)/ln(a) log_a(x) Trigonometric Functions sin(x) sin(x) cos(x) cos(x) tan(x) tan(x), tg(x) cot(x) cot(x), ctg(x) sec(x) sec(x) csc(x) csc(x), cosec(x) Inverse Trigonometric Functions asin(x), arcsin(x), sin^-1(x) asin(x) acos(x), arccos(x), cos^-1(x) acos(x) atan(x), arctan(x), tan^-1(x) atan(x) acot(x), arccot(x), cot^-1(x) acot(x) asec(x), arcsec(x), sec^-1(x) asec(x) acsc(x), arccsc(x), csc^-1(x) acsc(x) Hyperbolic Functions sinh(x) sinh(x) cosh(x) cosh(x) tanh(x) tanh(x) coth(x) coth(x) 1/cosh(x) sech(x) 1/sinh(x) csch(x) Inverse Hyperbolic Functions asinh(x), arcsinh(x), sinh^-1(x) asinh(x) acosh(x), arccosh(x), cosh^-1(x) acosh(x) atanh(x), arctanh(x), tanh^-1(x) atanh(x) acoth(x), arccoth(x), cot^-1(x) acoth(x) acosh(1/x) asech(x) asinh(1/x) acsch(x) Enter a function f(t) : For Inverse Laplace Transform, see Inverse Laplace Transform calculator. Write all suggestions in comments below. Your input: find $$\mathcal{L}\left(e^{2 t} \sin{\left (5 t \right )}\right)$$$.

$$\mathcal{L}\left(e^{2 t} \sin{\left (5 t \right )}\right)=\frac{5}{\left(s - 2\right)^{2} + 25}$$\$.