# How do you find the integral of Ex 3?

## How do you find the integral of Ex 3?

∫ex3dx=∫(+∞∑n=0x3nn!) dx=c++∞∑n=0x3n+1(3n+1)n! and this is well defined because the function f(t)=e−tt−23 is such that for t→0 it holds f(t)≈t−23 , so that the improper integral ∫s0f(t)dt is finite (I call s=−y3 ).

**How do you integrate an ex?**

What is the Integral of e^x? The integral of ex is ex + C. Symbolically it is written as ∫ ex dx = ex + C, where C is the integration constant.

**What is the integration of 3?**

Integration Rules

Common Functions | Function | Integral |
---|---|---|

Square | ∫x2 dx | x3/3 + C |

Reciprocal | ∫(1/x) dx | ln|x| + C |

Exponential | ∫ex dx | ex + C |

∫ax dx | ax/ln(a) + C |

### What is constant of integration?

noun Mathematics. a constant that is added to the function obtained by evaluating the indefinite integral of a given function, indicating that all indefinite integrals of the given function differ by, at most, a constant.

**How do you evaluate the integral E x 3?**

You can integrate term by term to find a series representation of the antiderivative (which converges on the entire complex plane, since e x 3 is an entire function). can be evaluated for any n > 0, and is equal to Γ ( ( n + 1) / n). The integral cannot be evaluated.

**What integrals does the integral calculator support?**

The Integral Calculator supports definite and indefinite integrals (antiderivatives) as well as integrating functions with many variables. You can also check your answers! Interactive graphs/plots help visualize and better understand the functions. For more about how to use the Integral Calculator, go to ” Help ” or take a look at the examples.

## How does Wolfram|Alpha do integrals?

Wolfram|Alpha computes integrals differently than people. It calls Mathematica’s Integrate function, which represents a huge amount of mathematical and computational research. Integrate does not do integrals the way people do. Instead, it uses powerful, general algorithms that often involve very sophisticated math.

**How does xmaxima calculate integrals?**

Maxima takes care of actually computing the integral of the mathematical function. Maxima’s output is transformed to LaTeX again and is then presented to the user. The antiderivative is computed using the Risch algorithm, which is hard to understand for humans. That’s why showing the steps of calculation is very challenging for integrals.