Question

$\int 3^{2x-7}dx=$

• A. $\frac{3^{2x-7}}{2\log 3}+c$
• B. $\frac{3^{2x-7}}{\log 3}+c$
• C. $\frac{3^{2x-7}}{\log 7}+c$
• D. $\frac{3^{2x-7}}{3\log 7}+c$

Answer 1

The correct option is A $\frac{3^{2x-7}}{2\log 3}+c$

$\int 3^{2x-7}dx$

Substitute $2x-7=t$

$\Rightarrow 2dx=dt$

$dx=\frac{1}{2}dt$

$\frac{1}{2}\int 3^{t}dt=\frac{1}{2}\frac{3^t}{\log 3}+c$

$=\frac{1}{2}\frac{3{}^{2x-7}}{\log 3}+c$

$\int 3{}^{2x-7}dx.=\frac{3{}^{2x-7}}{2\log 3}+c$