Evaluate the integrals in Exercises 31–78.
77. ∫dt/((t+1...

Question

Evaluate the integrals in Exercises 31–78.

77. ∫dt/((t+1)√(t²+2t-8))

Accepted Answer

Welcome back everyone. Evaluate the integral dx divided by x + 2 square root of x2 + 4 x minus 5. We will begin this problem by completing the square under the radical. We are given x2 + 4 x minus 5, which can be written as x2 + 4 x + 4 minus 9, which is x + 22 minus 32, right. And then we can rewrite the integral as follows that would be integral of d x divided by x + 2 square root of. So let's add the radical sign. And we have x + 22 minus 32. From here we will introduce a substitution. Let's suppose that u is equal to x + 2, and then we can show that d u is equal to dx, right, because the derivative of x + 2 is 1. And therefore we can rewrite the integral in terms of u and d u. That would be the integral of d u divided by u square root of u2 minus 32. From here we can use the standard integral, right? The integral of duu divided by u square root of u2 minus a 2. The value of this integral is going to be 1 divided by A. So in this case, A is 3, right? So we get 1/3. Inverse of 2 of the absolute value of u divided by a where a is 3. Plus a constant of integration c and finally let's replace u with x + 2 to get 1/3 inverse of 2 of the absolute value of x + 2 divided by 3. Plus C. That's our final answer and thank you for watching.

Evaluate the integrals in Exercises 31–78.77. ∫dt/((t+1)√(t²+2t-8))

Watch next

Evaluate the integrals in Exercises 31–78.
77. ∫dt/((t+1)√(t²+2t-8))