Question

\[ \int_{0}^{1}(0.001)^{x / 3} \cdot e^{x} d x= \] (A) \( \frac{e-10}{10\left(1-\log _{e} 10\right)} \) (B) \( \frac{10-10 e}{\left(1+\log _{e} 10\right)} \) (C) \( \frac{10-e}{e\left(1-\log _{e} 10\right)} \) (D) \( \frac{e-10}{10\left(1+\log _{e} 10\right)} \)

Answer 1

https://www.sarthaks.com/?qa=blob&qa_blobid=12383963833726324317

Let u = x( 1- log10 ) then du = ( 1- log10 ) dx 

Update limits: 

When x = 0 , u = 0 

When x = 1 , u = (1-log10)