What is the integral of x^20.4^{-x} ?

The integral of x^20.4^{-x} is 1.09135…*0.4^{-x}x^2-2.18271…(1.09135…*0.4^{-x}x-1.19105…*0.4^{-x})+C

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integral of x^20.4^{-x}

\int x^{2} 0. 4^{- x} d x

1.09135 \dots \cdot 0. 4^{- x} x^{2} - 2.18271 \dots (1.09135 \dots \cdot 0. 4^{- x} x - 1.19105 \dots \cdot 0. 4^{- x}) + C

Solution steps

\int x^{2} \cdot 0. 4^{- x} d x

Apply Integration By Parts

= 1.09135 \dots \cdot 0. 4^{- x} x^{2} - \int 2.18271 \dots \cdot 0. 4^{- x} x d x

\int 2.18271 \dots \cdot 0. 4^{- x} x d x = 2.18271 \dots (1.09135 \dots \cdot 0. 4^{- x} x - 1.19105 \dots \cdot 0. 4^{- x})

= 1.09135 \dots \cdot 0. 4^{- x} x^{2} - 2.18271 \dots (1.09135 \dots \cdot 0. 4^{- x} x - 1.19105 \dots \cdot 0. 4^{- x})

Add a constant to the solution

= 1.09135 \dots \cdot 0. 4^{- x} x^{2} - 2.18271 \dots (1.09135 \dots \cdot 0. 4^{- x} x - 1.19105 \dots \cdot 0. 4^{- x}) + C

\int \frac{y ^{2}}{( 4 - y ^{2} ) ^{\frac{3}{2}}} d y

t an g e n t f (x) = - 18 x - \frac{17}{x}

\int \frac{x ^{2}}{( 1 + x ^{3} ) ^{2}} d x

\frac{d}{d x} (e^{- y x})

(4 e^{2 x} + 2 x y - y^{2}) d x + (x - y)^{2} d y = 0

What is the integral of x^20.4^{-x} ?
The integral of x^20.4^{-x} is 1.09135…*0.4^{-x}x^2-2.18271…(1.09135…*0.4^{-x}x-1.19105…*0.4^{-x})+C