integral of 2^{7x+3}

解答

\int 2^{7 x + 3} d x

\frac{2 ^{7 x + 3}}{7 ln ( 2 )} + C

求解步骤

\int 2^{7 x + 3} d x

2^{7 x + 3} = 2^{3} \cdot 2^{7 x}

= \int 2^{3} \cdot 2^{7 x} d x

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2^{3} \cdot \int 2^{7 x} d x

化简

= 8 \cdot \int 2^{7 x} d x

化简

2^{7 x} : 12 8^{x}

= 8 \cdot \int 12 8^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= 8 \cdot \frac{12 8 ^{x}}{ln ( 128 )}

化简

8 \cdot \frac{12 8 ^{x}}{ln ( 128 )} : \frac{2 ^{7 x + 3}}{7 ln ( 2 )}

= \frac{2 ^{7 x + 3}}{7 ln ( 2 )}

解答补常数

= \frac{2 ^{7 x + 3}}{7 ln ( 2 )} + C

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