Integrate the function. 8) ∫(7 dx)/(√(4 + 49x^2)) 9)...

Transcript

00:01 We want to integrate this function.

00:03 Let's use partial fraction.

00:04 So we're going to let the function va over x plus vx plus c over x squared plus 4 plus d x plus e over x square plus 4 square because x squared plus 4 is a repeated root.

00:26 Cross the denominator up to the right side.

00:29 You will get this.

00:47 I'm going to let x be 0.

00:50 When you sub in the x equals to 0, you'll get this.

00:56 So a is 1 over 16.

00:59 I'm going to let x be 1.

01:01 When you sub into here, you will rearrangeing, you'll get this.

01:13 When i let xb minus 1, it is very tedious, but just be patient and do it.

01:25 We will have to do it five times, so we get simultaneous equation because we have five unknowns.

01:42 Last one.

01:45 You can choose any values of x and just sub in and patiently simplify into a equation.

01:55 All you need is five of them.

01:59 All right.

02:00 So solving all of them, you will get b is minus 1 over 16, c is 0, d is minus 1 quarter, e is 0.

02:15 So i'm ready to sum my function here into its partial fraction and you will get this 1 over 16x minus x 16 x square plus 4 minus x 4 x square plus 4 square square x x okay so for the first time is easy to integrate second term i'm looking to for it to fit into this form of f prime over fx, if it fits into this form, i can use the result of non -bought of fx.

03:11 So if this is being fx, the f prime be 2x.

03:16 So i need a 2 here.

03:17 So i put a half here...

Question

Integrate the function. 8) \int \frac{7 \text{dx}}{\sqrt{4 + 49x^2}} 9) \int \frac{\text{dx}}{\sqrt{64 - x^2}}

Question

Integrate the function. 8) \int \frac{7 \text{dx}}{\sqrt{4 + 49x^2}} 9) \int \frac{\text{dx}}{\sqrt{64 - x^2}}

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