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Exercise

$\int_0^x\frac{e^x}{x}dx$

Step-by-step Solution

1

The integral $\int\frac{e^x}{x}dx$ is called 'exponential integral' and is non-elementary. The formula for the exponential integral is: $\int\frac{e^x}{x}=Ei(x)$, where $Ei$ is a special function on the complex plane

$\left[Ei\left(x\right)\right]_{0}^{x}$
2

Evaluate the definite integral

$Ei\left(x\right)-1Ei\left(0\right)$

Final answer to the exercise

$Ei\left(x\right)-1Ei\left(0\right)$

Try other ways to solve this exercise

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  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
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$\int_0^{\infty}\left(\frac{x}{x^3+1}\right)dx$

$\int_0^1\left(\frac{x}{1-x^2}\right)dx$

$\int_0^1\frac{dx}{\left(x+1\right)\left(x^2+1\right)}$

$\int_1^2\frac{1}{x\cdot\left(x+1\right)}dx$

Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

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