What is the integral of ∫ e^ (x^2 +sinx) dx ?

In summary, the integral is a mathematical concept used to find the total value of a changing quantity over a specific interval by representing the area under a curve on a graph. The notation ∫ signifies the integral sign and is followed by the function to be integrated and the variables of integration. The integral of ∫ e^ (x^2 +sinx) dx cannot be solved using a general method, but can be approximated or solved using special functions. The e^x function represents the rate of change of the function being integrated. The integral of ∫ e^ (x^2 +sinx) dx is related to the concept of area as it represents the area under the curve of the function and can be thought of as the
  • #1
eric_o6
1
0
What is the integral of ∫ e^ (x^2 +sinx) dx


I got the answer e^(x^2+sinx)/(2x+cosx) but I know that is wrong. I don't understand how you treat the + part for an e^() problem.
 
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  • #2
There is presumably no closed form solution involving elementary functions.

Mathematica agrees: http://integrals.wolfram.com/index.jsp?expr=e^(x^2+%2B+sin(x))&random=false
 

1. What is the concept of an integral?

The integral is a mathematical concept that represents the area under a curve on a graph. It is used to find the total value of a changing quantity over a specific interval.

2. What does the notation ∫ signify?

The notation ∫ represents the integral sign, which is used to denote that a function is being integrated. It is usually followed by the function to be integrated and the variables of integration.

3. How do you solve the integral of ∫ e^ (x^2 +sinx) dx ?

There is no general method to solve this integral, but it can be approximated using numerical methods or solved using special functions such as the error function.

4. What is the significance of the e^x function in this integral?

The e^x function, also known as the exponential function, is a mathematical function that is commonly used in mathematical models to represent growth or decay. In this integral, it represents the rate of change of the function being integrated.

5. How is the integral of ∫ e^ (x^2 +sinx) dx related to the concept of area?

The integral of ∫ e^ (x^2 +sinx) dx represents the area under the curve of the function e^ (x^2 +sinx). This area can be thought of as the sum of infinitely small rectangles, with the height of each rectangle determined by the function at that point. Thus, the integral is a way to find the total area under the curve.

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