Mister Exam

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Identical expressions
one /(nine *x^ two - seven)
1 divide by (9 multiply by x squared minus 7)
one divide by (nine multiply by x to the power of two minus seven)
1/(9*x2-7)
1/9*x2-7
1/(9*x²-7)
1/(9*x to the power of 2-7)
1/(9x^2-7)
1/(9x2-7)
1/9x2-7
1/9x^2-7
1 divide by (9*x^2-7)
1/(9*x^2-7)dx
Similar expressions
1/(9*x^2+7)

Integral of 1/(9*x^2-7) dx

The solution

You have entered [src]

  1            
  /            
 |             
 |     1       
 |  -------- dx
 |     2       
 |  9*x  - 7   
 |             
/              
0

$$\int\limits_{0}^{1} \frac{1}{9 x^{2} - 7}\, dx$$

Integral(1/(9*x^2 - 7), (x, 0, 1))

Detail solution

PiecewiseRule(subfunctions=[(ArctanRule(a=1, b=9, c=-7, context=1/(9*x**2 - 7), symbol=x), False), (ArccothRule(a=1, b=9, c=-7, context=1/(9*x**2 - 7), symbol=x), x**2 > 7/9), (ArctanhRule(a=1, b=9, c=-7, context=1/(9*x**2 - 7), symbol=x), x**2 < 7/9)], context=1/(9*x**2 - 7), symbol=x)

Add the constant of integration:

$\begin{cases} - \frac{\sqrt{7} \operatorname{acoth}{\left(\frac{3 \sqrt{7} x}{7} \right)}}{21} & \text{for}\: x^{2} > \frac{7}{9} \\- \frac{\sqrt{7} \operatorname{atanh}{\left(\frac{3 \sqrt{7} x}{7} \right)}}{21} & \text{for}\: x^{2} < \frac{7}{9} \end{cases}+ \mathrm{constant}$

The answer is:

$\begin{cases} - \frac{\sqrt{7} \operatorname{acoth}{\left(\frac{3 \sqrt{7} x}{7} \right)}}{21} & \text{for}\: x^{2} > \frac{7}{9} \\- \frac{\sqrt{7} \operatorname{atanh}{\left(\frac{3 \sqrt{7} x}{7} \right)}}{21} & \text{for}\: x^{2} < \frac{7}{9} \end{cases}+ \mathrm{constant}$

The answer (Indefinite) [src]

                     //            /      ___\               \
                     ||   ___      |3*x*\/ 7 |               |
                     ||-\/ 7 *acoth|---------|               |
  /                  ||            \    7    /        2      |
 |                   ||------------------------  for x  > 7/9|
 |    1              ||           21                         |
 | -------- dx = C + |<                                      |
 |    2              ||            /      ___\               |
 | 9*x  - 7          ||   ___      |3*x*\/ 7 |               |
 |                   ||-\/ 7 *atanh|---------|               |
/                    ||            \    7    /        2      |
                     ||------------------------  for x  < 7/9|
                     \\           21                         /

$$\int \frac{1}{9 x^{2} - 7}\, dx = C + \begin{cases} - \frac{\sqrt{7} \operatorname{acoth}{\left(\frac{3 \sqrt{7} x}{7} \right)}}{21} & \text{for}\: x^{2} > \frac{7}{9} \\- \frac{\sqrt{7} \operatorname{atanh}{\left(\frac{3 \sqrt{7} x}{7} \right)}}{21} & \text{for}\: x^{2} < \frac{7}{9} \end{cases}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

nan

$$\text{NaN}$$

nan

$$\text{NaN}$$

nan

Numerical answer [src]

-0.122200289921172

-0.122200289921172

Use the examples entering the upper and lower limits of integration.

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Identical expressions

Similar expressions

Integral of 1/(9*x^2-7) dx

Limits of integration:

The graph:

Piecewise:

The solution