Intereting Posts

Prove that for any square matrix, an invertible matrix B exists, so that BA is triangular
Why is it “easier” to work with function fields than with algebraic number fields?
Determinant of an $n\times n$ complex matrix as an $2n\times 2n$ real determinant
Is $\frac{d}{dx}\left(\sum_{n = 0}^\infty x^n\right) = \sum_{n = 0}^\infty\left(\frac{d}{dx} x^n \right)$ true?
Weak convergences of measurable functions and of measures
If every vector is an eigenvector, the operator must be a scalar multiple of the identity operator?
Is it possible to use regularization methods on the Harmonic Series?
Automorphism group of the quaternion group
$\angle ABD=38°, \angle DBC=46°, \angle BCA=22°, \angle ACD=48°,$ then find $\angle BDA$
How to prove that Riemann zeta function is zero for negative even numbers?
Projection of a 3D spherical distribution function in to a 2D cartesian plane
On radial limits of Blaschke Products
Find primitive element such that conductor is relatively prime to an ideal (exercise from Neukirch)
The fibers of a finite morphism of affine varieties are all finite
Are there nontrivial continuous maps between complex projective spaces?

I am trying to simplify of this:

$$\int_{0}^{\infty} \frac{1-e^{-x}}{x}e^{-\lambda x}\,dx.$$

Maybe I should separate these equation into two exponential integral function?

But it will ended up with infinite minus infinite?

please give me some help or advices, thanks!

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- Why is $e$ so special?
- Solve equation $\exp(ax)+\exp(bx)=1$
- Intuitive Understanding of the constant “$e$”
- $e$ is the only number in the universe having this property?
- Exponential of powers of the derivative operator

- Why does integrating a complex exponential give the delta function?
- Is $e$ a coincidence?
- For a fixed complex number $z$, if $z_{n}=\left( 1+\frac{z}{n}\right)^{n}$. Find $\lim_{n \to \infty}|z_{n}|$
- Proof that $6^n$ always has a last digit of $6$
- Modular Arithmetic with Powers and Large Numbers
- Radius of convergence for the exponential function
- how to prove that $\lim\limits_{n\to\infty} \left( 1-\frac{1}{n} \right)^n = \frac{1}{e}$
- Square and square root and negative numbers
- What is $(-1)^{\frac{2}{3}}$?
- Prove that for any nonnegative integer n the number $5^{5^{n+1}} + 5^{5 ^n} + 1$ is not prime

Write ${1-e^{-x}\over x}$ as $\int_0^1 e^{-tx}\,dt$, reverse the order of integration in the resulting double integral, then integrate.

- Notions of equivalent metrics
- Interesting properties of Fibonacci-like sequences?
- Convergence of the series $\sum_ {n\geq1} \frac {(f(n) +P(n)) \pmod {Q(n)}} {D(n)}$
- Strangest Notation?
- How to find all subgroups of a group in GAP
- Compound Distribution — Log Normal Distribution with Normally Distributed Mean
- Prove$ L^2$ inner product satisfies positivity
- multiplicative group of infinite fields
- Can RUBIK's cube be solved using group theory?
- Is this:$\sum_{n=1}^{\infty}{(-1)}^{\frac{n(n-1)}{2}}\frac{1}{n}$ a convergent series?
- Proving $\sum_{k=0}^{2m}(-1)^k{\binom{2m}{k}}^3=(-1)^m\binom{2m}{m}\binom{3m}{m}$ (Dixon's identity)
- Which of the numbers $1, 2^{1/2}, 3^{1/3}, 4^{1/4}, 5^{1/5}, 6^{1/6} , 7^{1/7}$ is largest, and how to find out without calculator?
- What is the minimum value of $(1 + a_1)(1 + a_2). . .(1 + a_n)$?
- Proving that the dual of the $\mathcal{l}_p$ norm is the $\mathcal{l}_q$ norm.
- Showing that two definitions of $\limsup$ are equivalent