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How do you in partial fractions?:
log((6*x-10*sqrt(3))/(10*sqrt(3)+6*x))/(10*sqrt(3))
log((4*x-2^(3/2))/(2^(3/2)+4*x))/2^(5/2)
-log(((4*sin(x))/(1+cos(x))-sqrt(17)+1)/(1+sqrt(17)+(4*sin(x))/(1+cos(x))))/sqrt(17)
log((4*x-sqrt(41)-7)/((-7)+sqrt(41)+4*x))/sqrt(41)
Factor polynomial:
x^4+x²-20
x^4-b^4
x^4+9*x^2+3^4
x^4+8*3^0.5*i+8
Least common denominator:
sin(x+pi/8)+sin(pi/8)
(-sin(x)/cos(2*x)^(1/4)+cos(x)*sin(2*x)/(2*cos(2*x)^(5/4)))/(1+cos(x)^2/sqrt(cos(2*x)))
sin(x+a/2)*sin(x)/sin(a/2)
sin(x)^2*cos(x)/(2-sin(x))^2+2*cos(x)*sin(x)/(2-sin(x))
Factor squared:
-y^2-4*y*x+12*x^2
y^2+4*y*x+12*x^2
-y^2-4*y+8
y^2-4*y*q-q^2
Least common denominator:
log((4*x-sqrt(41)-7)/((-7)+sqrt(41)+4*x))/sqrt(41)
Identical expressions
log((four *x-sqrt(forty-one)- seven)/((- seven)+sqrt(forty-one)+ four *x))/sqrt(forty-one)
logarithm of ((4 multiply by x minus square root of (41) minus 7) divide by (( minus 7) plus square root of (41) plus 4 multiply by x)) divide by square root of (41)
logarithm of ((four multiply by x minus square root of (forty minus one) minus seven) divide by (( minus seven) plus square root of (forty minus one) plus four multiply by x)) divide by square root of (forty minus one)
log((4*x-√(41)-7)/((-7)+√(41)+4*x))/√(41)
log((4x-sqrt(41)-7)/((-7)+sqrt(41)+4x))/sqrt(41)
log4x-sqrt41-7/-7+sqrt41+4x/sqrt41
log((4*x-sqrt(41)-7) divide by ((-7)+sqrt(41)+4*x)) divide by sqrt(41)
Similar expressions
log((4*x-sqrt(41)-7)/((-7)+sqrt(41)-4*x))/sqrt(41)
log((4*x-sqrt(41)-7)/((7)+sqrt(41)+4*x))/sqrt(41)
log((4*x+sqrt(41)-7)/((-7)+sqrt(41)+4*x))/sqrt(41)
log((4*x-sqrt(41)+7)/((-7)+sqrt(41)+4*x))/sqrt(41)
log((4*x-sqrt(41)-7)/((-7)-sqrt(41)+4*x))/sqrt(41)

Expression simplification/ Fraction Decomposition into the simple/ log((4*x-sqrt(41)-7)/((-7)+sqrt(41)+4*x))/sqrt(41)

How do you log((4x-sqrt(41)-7)/((-7)+sqrt(41)+4x))/sqrt(41) in partial fractions?

The solution

You have entered [src]

   /         ____    \
   | 4*x - \/ 41  - 7|
log|-----------------|
   |       ____      |
   \-7 + \/ 41  + 4*x/
----------------------
          ____        
        \/ 41

$$\frac{\log{\left(\frac{\left(4 x - \sqrt{41}\right) - 7}{4 x + \left(-7 + \sqrt{41}\right)} \right)}}{\sqrt{41}}$$

log((4*x - sqrt(41) - 7)/(-7 + sqrt(41) + 4*x))/sqrt(41)

Fraction decomposition [src]

sqrt(41)*log(-7/(-7 + sqrt(41) + 4*x) - sqrt(41)/(-7 + sqrt(41) + 4*x) + 4*x/(-7 + sqrt(41) + 4*x))/41

$$\frac{\sqrt{41} \log{\left(\frac{4 x}{4 x + \left(-7 + \sqrt{41}\right)} - \frac{7}{4 x + \left(-7 + \sqrt{41}\right)} - \frac{\sqrt{41}}{4 x + \left(-7 + \sqrt{41}\right)} \right)}}{41}$$

          /                              ____                         \
  ____    |          7                 \/ 41                4*x       |
\/ 41 *log|- ----------------- - ----------------- + -----------------|
          |         ____                ____                ____      |
          \  -7 + \/ 41  + 4*x   -7 + \/ 41  + 4*x   -7 + \/ 41  + 4*x/
-----------------------------------------------------------------------
                                   41

General simplification [src]

          /       ____      \
  ____    |-7 - \/ 41  + 4*x|
\/ 41 *log|-----------------|
          |       ____      |
          \-7 + \/ 41  + 4*x/
-----------------------------
              41

$$\frac{\sqrt{41} \log{\left(\frac{4 x - 7 - \sqrt{41}}{4 x - 7 + \sqrt{41}} \right)}}{41}$$

sqrt(41)*log((-7 - sqrt(41) + 4*x)/(-7 + sqrt(41) + 4*x))/41

Common denominator [src]

          /                              ____                         \
  ____    |          7                 \/ 41                4*x       |
\/ 41 *log|- ----------------- - ----------------- + -----------------|
          |         ____                ____                ____      |
          \  -7 + \/ 41  + 4*x   -7 + \/ 41  + 4*x   -7 + \/ 41  + 4*x/
-----------------------------------------------------------------------
                                   41

$$\frac{\sqrt{41} \log{\left(\frac{4 x}{4 x - 7 + \sqrt{41}} - \frac{7}{4 x - 7 + \sqrt{41}} - \frac{\sqrt{41}}{4 x - 7 + \sqrt{41}} \right)}}{41}$$

sqrt(41)*log(-7/(-7 + sqrt(41) + 4*x) - sqrt(41)/(-7 + sqrt(41) + 4*x) + 4*x/(-7 + sqrt(41) + 4*x))/41

Trigonometric part [src]

          /       ____      \
  ____    |-7 - \/ 41  + 4*x|
\/ 41 *log|-----------------|
          |       ____      |
          \-7 + \/ 41  + 4*x/
-----------------------------
              41

$$\frac{\sqrt{41} \log{\left(\frac{4 x - 7 - \sqrt{41}}{4 x - 7 + \sqrt{41}} \right)}}{41}$$

sqrt(41)*log((-7 - sqrt(41) + 4*x)/(-7 + sqrt(41) + 4*x))/41

Powers [src]

          /       ____      \
  ____    |-7 - \/ 41  + 4*x|
\/ 41 *log|-----------------|
          |       ____      |
          \-7 + \/ 41  + 4*x/
-----------------------------
              41

$$\frac{\sqrt{41} \log{\left(\frac{4 x - 7 - \sqrt{41}}{4 x - 7 + \sqrt{41}} \right)}}{41}$$

sqrt(41)*log((-7 - sqrt(41) + 4*x)/(-7 + sqrt(41) + 4*x))/41

Rational denominator [src]

          / /      ____      \ \
  ____    |-\7 + \/ 41  - 4*x/ |
\/ 41 *log|--------------------|
          |        ____        |
          \ -7 + \/ 41  + 4*x  /
--------------------------------
               41

$$\frac{\sqrt{41} \log{\left(- \frac{- 4 x + \sqrt{41} + 7}{4 x - 7 + \sqrt{41}} \right)}}{41}$$

sqrt(41)*log(-(7 + sqrt(41) - 4*x)/(-7 + sqrt(41) + 4*x))/41

Assemble expression [src]

          /         ____    \
  ____    | 4*x - \/ 41  - 7|
\/ 41 *log|-----------------|
          |       ____      |
          \-7 + \/ 41  + 4*x/
-----------------------------
              41

$$\frac{\sqrt{41} \log{\left(\frac{\left(4 x - \sqrt{41}\right) - 7}{4 x + \left(-7 + \sqrt{41}\right)} \right)}}{41}$$

sqrt(41)*log((4*x - sqrt(41) - 7)/(-7 + sqrt(41) + 4*x))/41

Numerical answer [src]

0.156173761888606*log((4*x - sqrt(41) - 7)/(-7 + sqrt(41) + 4*x))

0.156173761888606*log((4*x - sqrt(41) - 7)/(-7 + sqrt(41) + 4*x))

Combining rational expressions [src]

          /       ____      \
  ____    |-7 - \/ 41  + 4*x|
\/ 41 *log|-----------------|
          |       ____      |
          \-7 + \/ 41  + 4*x/
-----------------------------
              41

$$\frac{\sqrt{41} \log{\left(\frac{4 x - 7 - \sqrt{41}}{4 x - 7 + \sqrt{41}} \right)}}{41}$$

sqrt(41)*log((-7 - sqrt(41) + 4*x)/(-7 + sqrt(41) + 4*x))/41

Combinatorics [src]

          /                              ____                         \
  ____    |          7                 \/ 41                4*x       |
\/ 41 *log|- ----------------- - ----------------- + -----------------|
          |         ____                ____                ____      |
          \  -7 + \/ 41  + 4*x   -7 + \/ 41  + 4*x   -7 + \/ 41  + 4*x/
-----------------------------------------------------------------------
                                   41

$$\frac{\sqrt{41} \log{\left(\frac{4 x}{4 x - 7 + \sqrt{41}} - \frac{7}{4 x - 7 + \sqrt{41}} - \frac{\sqrt{41}}{4 x - 7 + \sqrt{41}} \right)}}{41}$$

sqrt(41)*log(-7/(-7 + sqrt(41) + 4*x) - sqrt(41)/(-7 + sqrt(41) + 4*x) + 4*x/(-7 + sqrt(41) + 4*x))/41

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How do you log((4*x-sqrt(41)-7)/((-7)+sqrt(41)+4*x))/sqrt(41) in partial fractions?

The solution

How do you log((4x-sqrt(41)-7)/((-7)+sqrt(41)+4x))/sqrt(41) in partial fractions?