We're going to take this equation and multiply by its conjugate in the denominator. So we get sqrt 1 plus sine 3X. And if we do it to the denominator, we're going to do the same thing to the numerator. So what this does is it gives me zero to π eighteenths of cosine 43X square root 1 plus sine 3 XDX all over sqrt 1 minus sine squared 3X. Well, we know that one minus sine squared is really cosine squared. Square root of cosine squared is a single cosine, and so one cosine with the four cosines in the numerator will simplify down to three cosines in the numerator. So we get cosine cubed 3X times the square root 1 plus sine 3X DX. So if we pull out a cosine 3X and then we switch the remaining cosine squareds to 1 minus sine squared 3X, we still have sqrt 1 plus sine 3X DX. So from here if we thought about letting U equals sine 3X, then we would have DU equaling 3 cosine 3X DX or 1/3 DU would equal cosine 3X DX. So at this step we're going to have sine of 0 is going to be 0, sine of 3 * π eighteenth or sine of Pi six would be 1/2 the cosine 3X DX we need as our 1/3 DU portion. So we end up with one third 1 -, U ^2 sqrt 1 plus udu. From here we might do another sub. Let's let V equal 1 + U. So if we have V equaling one plus UV -1 would equal U, so and our DV would just equal DU. So now we'd have one third 1 -, U ^2 would be 1 minus the quantity v -, 1 ^2 sqrt v DV. If I change my bounds, I get 0 + 1 of 1/1 plus 1/2 three halves. So now if we combine this out, let's see 1 -, U, but U is v -, 1 ^2, so 1/3. Let's go ahead and foil that out and combine anything. So we get 1 -, v ^2 -, a negative 2V, so plus two V -, +1, which would give us a -1 square root of VDV so that one and -1 we can see are going to cancel. So now we'd have negative v ^2 + 2 V all Times Square root of V DB, and we could think of that as negative V to the five halves +2 V to the three halves DB. Remember, when we multiply and the bases are the same, we just add the exponents. So 2 + 1/2 is five halves, 1 + 1/2 is the three halves. Now I'm just going to use the power rule. So we're going to add 1 to the exponent, so 1/3 adding one to the exponent, we're going to get 7 halves, and we're going to divide by that new exponent or multiply by its reciprocal. We're going to add 1 V to the five halves, but we're going to multiply by 2/5, so two times the 2/5, and that's going to go from one to three halves, so 1/3 negative, 2 sevenths to the three halves. So three halves to the seven halves, three halves to the seven halves plus 4/5 * 3 halves to the five halves. And that whole thing is going to be. Then we have to take away sticking in one. So we get -2 sevenths plus 4/5. We continue to compute this. We get 1/3. I might take out of three halves from both of these terms, three halves to the five halves. Actually, I might take out three halves to the five halves because that would leave me a -2 sevenths times 13 halves plus A 4/5. And then back here, if we just get a common denominator, we get -10 + 28 / 35. So now it just doesn't matter of doing some plugging and chugging 3 halves to the five halves here, we're going to get -3 sevenths plus 4/5. So if we get a common denominator here, we'd have -15 + 28 / 35 minus. This was going to turn into 1830 fifths. So then three halves fifteen 1/3 three halves to the five halves times 13 / 35 -, 18 / 35. I could distribute the one third if I wanted three halves to the five halves times 13 / 105 -, 18 / 105.