Question

5^x / 2^x+1 интеграл​

Answer 1

(5^x/ln5)/((2^x/ln2)+x)= (ln2*5^x)/(ln5*2^x+ln5ln2x)

Answer 2

To integrate the expression ∫(5^x / 2^(x+1)) dx, we can use the properties of exponents and logarithms to simplify the expression and then evaluate the integral.

Let's start by manipulating the expression: 5^x / 2^(x+1) = (5/2)^(x) / 2 = (5/4)^(x)

Now we can integrate the simplified expression. The integral of (5/4)^x with respect to x can be found using the power rule of integration. The power rule states that the integral of x^n dx is (1/(n+1)) * x^(n+1), where n is any real number except -1.

Therefore, applying the power rule, the integral becomes: ∫(5/4)^x dx = (1/log(5/4)) * (5/4)^x + C

where C is the constant of integration.

So, the integral of 5^x / 2^(x+1) with respect to x is (1/log(5/4)) * (5/4)^x + C, where C is the constant of integration.