We're going to use one of our hyperbolic cosine identities, which says if I have a hyperbolic cosine squared, that really equals the hyperbolic cosine of twice the angle plus one all divided by two. So instead of hyperbolic cosine squared of five X / 2, that's going to be equivalent to hyperbolic cosine of five X + 1 all divided by two. Now we know that the derivative or the integral of hyperbolic cosine is hyperbolic sine. We have to take the derivative of the 5X because of the chain rule and divide by it. So we're going to have 5 * 2 in the denominator or 10, and then that 1/2 is going to have the integral turning into half X. We're going to put in our lower bound and our upper bound. We're going to realize that negative lane 2 / 5 we could really think of as lane of 1/2 / 5. Using our definition for hyperbolic sign, we're going to have E to the 5 * 0, which is just 0 -, E to the -5 * 0 once again, 0 / 2, and then over the 10 + 1/2 * 0. So that's my upper bound minus my lower bound. So I'm going to put in ELN half over 5 * 5 -, E to the negative Ln half over 5 * 5 all over 2 * 10 or 20 - 1/2. Now I'm going to use this negative Ln 2 / 5 part because the negative and the negative are going to make it a positive. So the E and the Ln cancel the five and the five cancel. This first term turns into half. This next term is going to turn into. You're going to bring the negative up into the exponent. So 1/2 to the -1 is 2. The fives will cancel the E to the Ln. So we have 1/2 -, 2 which is going to be -3 halves -3 halves divided by 20 is -3 fortieths and then a negative of -3 fortieths is +3 fortieths. For the second part, the negative and the negative cancel. So we get 1/2 lane 2 / 5 or 110th lane two. Now we could realize that this is oh it was a plus half X here. So then we have a negative here and the negative here and negative times negative makes that a positive. So we could think of 110th as 1/2 * 1/5 and bring the half up into the exponent if we wanted to. So we could get it to equal 340th plus 1/5 Ln sqrt 2 which is the answer they have there. I would guess that if we had typed in three 40th plus 110th LN2, it would have also accepted that answer.