What is x^rbx^{(b-1)}e^{-x^b}dx ?

The solution to x^rbx^{(b-1)}e^{-x^b}dx is be^{-x^b}x^{r+b-1}dx

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simplify x^rbx^{(b-1)}e^{-x^b}dx

simplify

x^{r} b x^{(b - 1)} e^{- x^{b}} d x

b e^{- x^{b}} x^{r + b - 1} d x

Solution steps

x^{r} b x^{(b - 1)} e^{- x^{b}} d x

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

x^{r} x^{b - 1} = x^{r + b - 1}

= b x^{r + b - 1} e^{- x^{b}} d x

9315 y 3 z

12 x^{5} \cdot 12 x^{7}

3 4 9^{2}

2 (6.67 \cdot 1 0^{- 11}) (5.97 \cdot 1 0^{24})

98 e^{- 0.07 (10)}

What is x^rbx^{(b-1)}e^{-x^b}dx ?
The solution to x^rbx^{(b-1)}e^{-x^b}dx is be^{-x^b}x^{r+b-1}dx