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Identical expressions
√(3x²-2x+ four)
√(3x² minus 2x plus 4)
√(3x² minus 2x plus four)
√3x²-2x+4
√(3x²-2x+4)dx
Similar expressions
√(3x²+2x+4)
√(3x²-2x-4)

Solving integrals/ √(3x²-2x+4)

Integral of √(3x²-2x+4) dx

The solution

You have entered [src]

  1                       
  /                       
 |                        
 |     ________________   
 |    /    2              
 |  \/  3*x  - 2*x + 4  dx
 |                        
/                         
0

$$\int\limits_{0}^{1} \sqrt{3 x^{2} - 2 x + 4}\, dx$$

Integral(sqrt(3*x^2 - 2*x + 4), (x, 0, 1))

Detail solution

SqrtQuadraticRule(a=4, b=-2, c=3, context=sqrt(3*x**2 - 2*x + 4), symbol=x)

Now simplify:

$\frac{\left(3 x - 1\right) \sqrt{3 x^{2} - 2 x + 4}}{6} + \frac{11 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{11} \cdot \left(3 x - 1\right)}{11} \right)}}{18}$
Add the constant of integration:

$\frac{\left(3 x - 1\right) \sqrt{3 x^{2} - 2 x + 4}}{6} + \frac{11 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{11} \cdot \left(3 x - 1\right)}{11} \right)}}{18}+ \mathrm{constant}$

The answer is:

$\frac{\left(3 x - 1\right) \sqrt{3 x^{2} - 2 x + 4}}{6} + \frac{11 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{11} \cdot \left(3 x - 1\right)}{11} \right)}}{18}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                                           /    ____           \
 |                                                                   ___      |3*\/ 11 *(-1/3 + x)|
 |    ________________             ________________             11*\/ 3 *asinh|-------------------|
 |   /    2                       /              2  /  1   x\                 \         11        /
 | \/  3*x  - 2*x + 4  dx = C + \/  4 - 2*x + 3*x  *|- - + -| + -----------------------------------
 |                                                  \  6   2/                    18                
/

$${{11\,{\rm asinh}\; \left({{6\,x-2}\over{2\,\sqrt{11}}}\right) }\over{2\,3^{{{3}\over{2}}}}}+{{x\,\sqrt{3\,x^2-2\,x+4}}\over{2}}-{{ \sqrt{3\,x^2-2\,x+4}}\over{6}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

                          /  ____\                 /    ____\
                 ___      |\/ 11 |        ___      |2*\/ 11 |
      ___   11*\/ 3 *asinh|------|   11*\/ 3 *asinh|--------|
1   \/ 5                  \  11  /                 \   11   /
- + ----- + ---------------------- + ------------------------
3     3               18                        18

$${{11\,\sqrt{3}\,{\rm asinh}\; \left({{2}\over{\sqrt{11}}}\right)+6 \,\sqrt{5}}\over{18}}+{{11\,\sqrt{3}\,{\rm asinh}\; \left({{1}\over{ \sqrt{11}}}\right)+6}\over{18}}$$

                          /  ____\                 /    ____\
                 ___      |\/ 11 |        ___      |2*\/ 11 |
      ___   11*\/ 3 *asinh|------|   11*\/ 3 *asinh|--------|
1   \/ 5                  \  11  /                 \   11   /
- + ----- + ---------------------- + ------------------------
3     3               18                        18

$$\frac{11 \sqrt{3} \operatorname{asinh}{\left(\frac{\sqrt{11}}{11} \right)}}{18} + \frac{1}{3} + \frac{11 \sqrt{3} \operatorname{asinh}{\left(\frac{2 \sqrt{11}}{11} \right)}}{18} + \frac{\sqrt{5}}{3}$$

Simplify

Numerical answer [src]

1.99801282141864

1.99801282141864

The graph

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

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Identical expressions

Similar expressions

Integral of √(3x²-2x+4) dx

Limits of integration:

The graph:

Piecewise:

The solution