Answer to Question #162049 in Calculus for Phyroe

Question

Evaluate the integral of 5^(2y) dy

Answer 1

Evaluate $\int$ 5^2y dy

Solution

$\int$ 5^2y dy = $\int$ 25^y dy

Apply exponential rule: $\int$ a^y dy = (a^y)/(ln a) Where a = 25 in this case

Hence $\int$ 25^y dy = (25^y)/(ln 25)

Simplyfying: $\int$ 25^y dy = (25^y)/(2ln 5)

Adding the integral constant C: $\int$ 25^y dy = (25^y)/(2ln 5) + C

Answer: $\int$ 5^2y dy = (25^y)/(2ln 5) + C