Help with one integral problem?

Question

asked May 7, 2021 28.8k views

1 Answer

Abhshkdz · Answer 1 · 2021-05-11T01:33:56+0000

Answer:
2√(1+tant)+C

Explanation:

To integrate means to find the antiderivative of the function. For this problem, we can use u-substitution.

$\int\limits {(dt)/(cos^2t√(1+tant) ) } \$

Let's first use our identities to rewrite the function. Since
(1)/(cosx) =secx , we can use this identity.

$\int\limits {(sec^2t)/(√(1+tant) ) } \,$

u=√(1+tant)

du=(sec^2t)/(2√(1+tant) ) dt

Now that we have u and du, we can plug them back in.

$\int\limits {2} \, du$

$\int\limits{2} \, du=2u$

Since we know u, we can plug that in.

2√(1+tant)

This may seem like the correct answer, but we forgot to add the constant.

2√(1+tant)+C