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Solving integrals/ y^2e^xy^2+6x

You entered:

y^2e^xy^2+6x

What you mean?

y^2*e^x*y^2 + 6*x
 
y^((2*e)^((x*y)^2)) + 6*x
 
y^((2*e)^((x*y)^2)) + 6*x

Integral of y^2e^xy^2+6x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                    
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 |  / 2  x  2      \   
 |  \y *e *y  + 6*x/ dx
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0
∫01(y2y2ex+6x) dx\int\limits_{0}^{1} \left(y^{2} y^{2} e^{x} + 6 x\right)\, dx
Simplify
Detail solution

  1. Integrate term-by-term:

    1. The integral of a constant times a function is the constant times the integral of the function:

      ∫6x dx=6∫x dx\int 6 x\, dx = 6 \int x\, dx

      1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

      So, the result is: 3x23 x^{2}

    1. The integral of a constant times a function is the constant times the integral of the function:

      ∫y2y2ex dx=y4∫ex dx\int y^{2} y^{2} e^{x}\, dx = y^{4} \int e^{x}\, dx

      1. The integral of the exponential function is itself.

        ∫ex dx=ex\int e^{x}\, dx = e^{x}

      So, the result is: y4exy^{4} e^{x}

    The result is: 3x2+y4ex3 x^{2} + y^{4} e^{x}

  2. Add the constant of integration:

    3x2+y4ex+constant3 x^{2} + y^{4} e^{x}+ \mathrm{constant}

The answer is:

3x2+y4ex+constant3 x^{2} + y^{4} e^{x}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                      
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 | / 2  x  2      \             2    4  x
 | \y *e *y  + 6*x/ dx = C + 3*x  + y *e 
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/
ex y4+3 x2e^{x}\,y^4+3\,x^2
Simplify
The answer [src] 
     4      4
3 - y  + e*y
(e−1) y4+3\left(e-1\right)\,y^4+3 
=
= 
     4      4
3 - y  + e*y
−y4+ey4+3- y^{4} + e y^{4} + 3
Simplify

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

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