Question

Help with one integral problem?

Answer 1

Answer: $2\sqrt{1+tant}+C$

Step-by-step explanation:

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

$\int\limits {\frac{dt}{cos^2t\sqrt{1+tant} } }$

Let's first use our identities to rewrite the function. Since $\frac{1}{cosx} =secx$, we can use this identity.

$\int\limits {\frac{sec^2t}{\sqrt{1+tant} } } \,$

$u=\sqrt{1+tant}$

$du=\frac{sec^2t}{2\sqrt{1+tant} } dt$

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.

$2\sqrt{1+tant}$

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

$2\sqrt{1+tant}+C$