First slide

Introduction to integration

Question

if $\int \frac{3^{x + 1} - 7^{x - 1}}{21^{x}} d x = K_{1} 3^{- x} + K_{2} 7^{- x} + C$ then

Easy

A

$K_{1} = \frac{1}{7 \log 3}, K_{2} = \frac{1}{3 \log 7}$
B

$K_{1} = \frac{1}{7 \log 3}, K_{2} = - \frac{1}{3 \log 7}$
C

$K_{1} = \frac{1}{7 \log 3}, K_{2} = - \frac{3}{\log 7}$
D

$k_{1} = \frac{3}{\log 7}, k_{2} = \frac{- 7}{\log 3}$

Solution

$\begin{array}{l} \int \frac{3^{x + 1} - 7^{x - 1}}{21^{x}} d x = 3 \int 7^{- x} d x - \frac{1}{7} \int 3^{- x} d x \\ = - 3 \frac{7^{- x}}{\log 7} + \frac{1}{7} \frac{3^{- x}}{\log 3} + C \end{array}$
$K_{1} = \frac{1}{7 \log 3}, K_{2} = - \frac{3}{\log 7}$

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