To integrate a function you find what the function you have is the derivative of. for example the derivative of x^2 is 2x. so the integral of 2x is x^2.
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You integrate each element of the matrix.
I assume you mean ex ? If so, by definition: ∫ex dx = ex + C Most calculus textbooks have a table of integrals which will list the integrals of other common forms of exponential & logarithmic functions.
to integrate something means to put two things together to make a new one
http://www.wolframalpha.com/input/?i=integrate+exp(x^2) The solution lists an "imaginary error function". This means that the integral can NOT be expressed as a finite number of the so-called elementary functions (that is, as any combination of addition, subtraction, multiplication, division, trigonometric functions, inverse trigonometric functions, exponential function, natural logarithm). The site mentioned also shows a series expansion.
In calculus, "to integrate" means to find the indefinite integrals of a particular function with respect to a certain variable using an operation called "integration". Synonyms for indefinite integrals are "primitives" and "antiderivatives". To integrate a function is the opposite of differentiating a function.