Question

calculate the indefinite integral

Answer 1

Answer:

e^x + 3^x/log3 - 2tanx

Step-by-step explanation:

By using simple rules of integration

Answer 2

Answer:

$\bold\red{{e}^{x}+\frac{{3}^{x}}{ln3}-2tanx+c}$

Step-by-step explanation:

We have to find the integration of,

$\int( {e}^{x} + {3}^{x} - \frac{2}{ {cos}^{2} x} )dx$

Further simplifying,

we get,

I =

$\int( {e}^{x} + {3}^{x} - 2 {sec}^{2} x)dx$

Now, we know that,

$\int {e}^{x} dx = {e}^{x}$

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

$\int {sec}^{2} x = tan \: x$

So,

putting the values,

we get,

Integration

$\bold{{e}^{x}+\frac{{3}^{x}}{ln3}-2tanx+c}$

where,

c is an arbitrary constant