Question

∫$2^{x}$ * $3^{x}$ dx

calculate the indefinite integral

Answer 1

Answer:

$\bold\red{\frac{ {6}^{x} }{ ln(6) } + c}$

Step-by-step explanation:

We have to integrate,

$\int {2}^{x} \times {3}^{x} dx$

We know that,

${a}^{m} \times {b}^{m} = {(ab)}^{m}$

Therefore,

we get,

$\int {(2 \times 3)}^{x} dx \\ \\ = \int {6}^{x} dx$

Now, we know that,

$\int {a}^{m} = \frac{ {a}^{m} }{ ln(a) }$

Therefore,

we get,

Integration

$= \bold{\frac{ {6}^{x} }{ ln(6) } + c}$

where,

c is an arbitrary constant