What is the integral of (3-x^2)0.2^x ?

The integral of (3-x^2)0.2^x is 0.62133…*0.2^xx^2+0.77211…*0.2^xx-1.38426…*0.2^x+C

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integral of (3-x^2)0.2^x

\int (3 - x^{2}) 0. 2^{x} d x

0.62133 \dots \cdot 0. 2^{x} x^{2} + 0.77211 \dots \cdot 0. 2^{x} x - 1.38426 \dots \cdot 0. 2^{x} + C

Solution steps

\int (3 - x^{2}) \cdot 0. 2^{x} d x

Expand

(3 - x^{2}) \cdot 0. 2^{x} : 3 \cdot 0. 2^{x} - 0. 2^{x} x^{2}

= \int 3 \cdot 0. 2^{x} - 0. 2^{x} x^{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 3 \cdot 0. 2^{x} d x - \int 0. 2^{x} x^{2} d x

\int 3 \cdot 0. 2^{x} d x = - 1.86400 \dots \cdot 0. 2^{x}

\int 0. 2^{x} x^{2} d x = - 0.62133 \dots \cdot 0. 2^{x} x^{2} + 1.24266 \dots (- 0.62133 \dots \cdot 0. 2^{x} x - 0.38605 \dots \cdot 0. 2^{x})

= - 1.86400 \dots \cdot 0. 2^{x} - (- 0.62133 \dots \cdot 0. 2^{x} x^{2} + 1.24266 \dots (- 0.62133 \dots \cdot 0. 2^{x} x - 0.38605 \dots \cdot 0. 2^{x}))

Simplify

- 1.86400 \dots \cdot 0. 2^{x} - (- 0.62133 \dots \cdot 0. 2^{x} x^{2} + 1.24266 \dots (- 0.62133 \dots \cdot 0. 2^{x} x - 0.38605 \dots \cdot 0. 2^{x})) : 0.62133 \dots \cdot 0. 2^{x} x^{2} + 0.77211 \dots \cdot 0. 2^{x} x - 1.38426 \dots \cdot 0. 2^{x}

= 0.62133 \dots \cdot 0. 2^{x} x^{2} + 0.77211 \dots \cdot 0. 2^{x} x - 1.38426 \dots \cdot 0. 2^{x}

Add a constant to the solution

= 0.62133 \dots \cdot 0. 2^{x} x^{2} + 0.77211 \dots \cdot 0. 2^{x} x - 1.38426 \dots \cdot 0. 2^{x} + C

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What is the integral of (3-x^2)0.2^x ?
The integral of (3-x^2)0.2^x is 0.62133…*0.2^xx^2+0.77211…*0.2^xx-1.38426…*0.2^x+C