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<img src="http://latex.codecogs.com/gif.latex?\int \sqrt{X^{2}  2X} dx =\int \sqrt{X^{2}  2X +1 1}dx =\int \sqrt{(X1)^2 1} dx
\\let X1 = \cosh \theta
\ \therefore\ dx = \sinh \theta d\theta
\\
\ \therefore\theta = \cosh^{1} (X1)
\\substitute in the integral
\\
\ \int\sqrt{\cosh \theta ^2 1} \sinh \theta d\theta
\\
\\ Remember \to \sinh ^{2}  cosh ^{2} = 1
\\
\ \therefore\int \sqrt{\sinh \theta ^2 } \sinh \theta d\theta = \int \(\sinh\theta )^{2} d\theta
 one year ago
 one year ago
<img src="http://latex.codecogs.com/gif.latex?\int \sqrt{X^{2}  2X} dx =\int \sqrt{X^{2}  2X +1 1}dx =\int \sqrt{(X1)^2 1} dx \\let X1 = \cosh \theta \ \therefore\ dx = \sinh \theta d\theta \\ \ \therefore\theta = \cosh^{1} (X1) \\substitute in the integral \\ \ \int\sqrt{\cosh \theta ^2 1} \sinh \theta d\theta \\ \\ Remember \to \sinh ^{2}  cosh ^{2} = 1 \\ \ \therefore\int \sqrt{\sinh \theta ^2 } \sinh \theta d\theta = \int \(\sinh\theta )^{2} d\theta
 one year ago
 one year ago

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