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What is integration of e raised to X?

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What is integration of e raised to X?

What is the Integral of e^x? The integral of ex is ex itself. But we know that we add an integration constant after the value of every indefinite integral and hence the integral of ex is ex + C. We write it mathematically as ∫ ex dx = ex + C.

What is antiderivative e?

Answer: The antiderivative of e2x is 1/2 e2x The integral of an exponential term eax is 1/a (eax) Explanation: On multiplying and dividing the function by 2, we get. ⇒ ∫ e2x = 1/2 ∫ 2e2x dx. ⇒ 1/2 ∫ e2x d(2x)

What is the antiderivative of e x 2?

2√π
Explanation: The function ex2 has an antiderivative, but there is no nice way to express it using elementary function. Saying that the antiderivative of ex2 is 2√π times the imaginary error function at x doesn’t help the intro student much, but that’s what it is.

What is the differentiation of E raised to negative x?

What is the differentiation of e raised to negative x? How to: Fix your dark spots. Surgeon explains at home fix for dark spots and uneven skin tones on skin. If you have to differentiate e^ (-x) with respect to x, then you can substitute (-x) = t. Then, dx = -dt. It depends on the variable with which it is differentiation is being done.

How to find the most general antiderivative?

Find the general antiderivative of a given function.

  • Explain the terms and notation used for an indefinite integral.
  • State the power rule for integrals.
  • Use antidifferentiation to solve simple initial-value problems.

    • How do you find the anti derivative?

    You can use reverse rules to find antiderivatives. The easiest antiderivative rules are the ones that are the reverse of derivative rules you already know. These are automatic, one-step antiderivatives with the exception of the reverse power rule, which is only slightly harder. You know that the derivative of sin x is cos x, so ]

    How do I find the most general antiderivative?

    If F is an antiderivative of f,then every antiderivative of f is of the form F(x)+C for some constant C.

  • Solving the initial-value problem dy dx = f(x),y(x0) = y0
  • requires us first to find the set of antiderivatives of f and then to look for the particular antiderivative that also satisfies the initial condition.