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Identical expressions
(x^ two + five)dx
(x squared plus 5)dx
(x to the power of two plus five)dx
(x2+5)dx
x2+5dx
(x²+5)dx
(x to the power of 2+5)dx
x^2+5dx
Similar expressions
(x^2-5)dx

Solving integrals/ (x^2+5)dx

Integral of (x^2+5)dx dx

The solution

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  1              
  /              
 |               
 |  / 2    \     
 |  \x  + 5/*1 dx
 |               
/                
0

$$\int\limits_{0}^{1} \left(x^{2} + 5\right) 1\, dx$$

Integral((x^2 + 5)*1, (x, 0, 1))

Detail solution

TrigSubstitutionRule(theta=_theta, func=sqrt(5)*tan(_theta), rewritten=5*sqrt(5)/cos(_theta)**4, substep=ConstantTimesRule(constant=5*sqrt(5), other=cos(_theta)**(-4), substep=RewriteRule(rewritten=(tan(_theta)**2 + 1)*sec(_theta)**2, substep=AlternativeRule(alternatives=[URule(u_var=_u, u_func=tan(_theta), constant=1, substep=AddRule(substeps=[PowerRule(base=_u, exp=2, context=_u**2, symbol=_u), ConstantRule(constant=1, context=1, symbol=_u)], context=_u**2 + 1, symbol=_u), context=(tan(_theta)**2 + 1)*sec(_theta)**2, symbol=_theta), RewriteRule(rewritten=tan(_theta)**2*sec(_theta)**2 + sec(_theta)**2, substep=AddRule(substeps=[URule(u_var=_u, u_func=tan(_theta), constant=1, substep=PowerRule(base=_u, exp=2, context=_u**2, symbol=_u), context=tan(_theta)**2*sec(_theta)**2, symbol=_theta), TrigRule(func='sec**2', arg=_theta, context=sec(_theta)**2, symbol=_theta)], context=tan(_theta)**2*sec(_theta)**2 + sec(_theta)**2, symbol=_theta), context=(tan(_theta)**2 + 1)*sec(_theta)**2, symbol=_theta), RewriteRule(rewritten=tan(_theta)**2*sec(_theta)**2 + sec(_theta)**2, substep=AddRule(substeps=[URule(u_var=_u, u_func=tan(_theta), constant=1, substep=PowerRule(base=_u, exp=2, context=_u**2, symbol=_u), context=tan(_theta)**2*sec(_theta)**2, symbol=_theta), TrigRule(func='sec**2', arg=_theta, context=sec(_theta)**2, symbol=_theta)], context=tan(_theta)**2*sec(_theta)**2 + sec(_theta)**2, symbol=_theta), context=(tan(_theta)**2 + 1)*sec(_theta)**2, symbol=_theta)], context=(tan(_theta)**2 + 1)*sec(_theta)**2, symbol=_theta), context=sec(_theta)**4, symbol=_theta), context=5*sqrt(5)/cos(_theta)**4, symbol=_theta), restriction=True, context=(x**2 + 5)*1, symbol=x)

Now simplify:

$\frac{x \left(x^{2} + 15\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} + 15\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} + 15\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                
 |                             /    ___     ___  3\
 | / 2    \                ___ |x*\/ 5    \/ 5 *x |
 | \x  + 5/*1 dx = C + 5*\/ 5 *|------- + --------|
 |                             \   5         75   /
/

$$\int \left(x^{2} + 5\right) 1\, dx = C + 5 \sqrt{5} \left(\frac{\sqrt{5} x^{3}}{75} + \frac{\sqrt{5} x}{5}\right)$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

16/3

$$\frac{16}{3}$$

16/3

$$\frac{16}{3}$$

Упростить

Numerical answer [src]

5.33333333333333

5.33333333333333

The graph

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

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Identical expressions

Similar expressions

Integral of (x^2+5)dx dx

Limits of integration:

The graph:

Piecewise:

The solution