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7.7.45Evaluate the integral.XcothdxXcoth dx7 In sinh7C7(Use C as the arbitrary constant.)

Question
Evaluate the integral.
 
Integral from nothing to nothing hyperbolic cotangent StartFraction x Over 7 EndFraction dx
Integral from nothing to nothing hyperbolic cotangent StartFraction x Over 7 EndFraction dx

equals7 ln left parenthesis hyperbolic sine StartFraction x Over 7 EndFraction right parenthesis plus Upper C

​(UseC as the arbitrary​constant.)
7.7.45
Evaluate the integral.
X
cothdx
X
coth dx7 In sinh
7
C
7
(Use C as the arbitrary constant.)
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7.7.45 Evaluate the integral. X cothdx X coth dx7 In sinh 7 C 7 (Use C as the arbitrary constant.)

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Step 1

Refer to the integral,

Rewrite the hyperbolic cotangent as,

х
cosh
7
coth
sinh
7
x
cosh
7
х
coth
7
sinh
7
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х cosh 7 coth sinh 7 x cosh 7 х coth 7 sinh 7

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Step 2

Assume the denominator as u,

x
u sinh
7
d
X
du
sinh
dx
7
1
du cosh
7
7
dx 7du
cosh
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x u sinh 7 d X du sinh dx 7 1 du cosh 7 7 dx 7du cosh

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Step 3

Now after substituting the value calculated in...

x
cosh
7
7
dx
x
-du
sinh
7
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x cosh 7 7 dx x -du sinh 7

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