integral of (3.2^x-2.3^x)/(2^x)

解

\int \frac{3. 2 ^{x} - 2. 3 ^{x}}{2 ^{x}} d x

2.12764 \dots \cdot 1. 6^{x} - 7.15502 \dots \cdot 1.1 5^{x} + C

解答ステップ

\int \frac{3. 2 ^{x} - 2. 3 ^{x}}{2 ^{x}} d x

拡張

\frac{3. 2 ^{x} - 2. 3 ^{x}}{2 ^{x}} : (\frac{3.2}{2})^{x} - (\frac{2.3}{2})^{x}

= \int (\frac{3.2}{2})^{x} - (\frac{2.3}{2})^{x} d x

総和規則を適用する:

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

= \int (\frac{3.2}{2})^{x} d x - \int (\frac{2.3}{2})^{x} d x

\int (\frac{3.2}{2})^{x} d x = 2.12764 \dots \cdot 1. 6^{x}

\int (\frac{2.3}{2})^{x} d x = 7.15502 \dots \cdot 1.1 5^{x}

= 2.12764 \dots \cdot 1. 6^{x} - 7.15502 \dots \cdot 1.1 5^{x}

定数を解答に追加する

= 2.12764 \dots \cdot 1. 6^{x} - 7.15502 \dots \cdot 1.1 5^{x} + C