Mister Exam

Other calculators

Solving integrals/ (1/x)+16*x*y^2

Integral of (1/x)+16*x*y^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                   
  /                   
 |                    
 |  /  1         2\   
 |  |1*- + 16*x*y | dx
 |  \  x          /   
 |                    
/                     
0
∫01(16xy2+1⋅1x) dx\int\limits_{0}^{1} \left(16 x y^{2} + 1 \cdot \frac{1}{x}\right)\, dx 
Integral(1/x + 16*x*y^2, (x, 0, 1))
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:

      ∫16xy2 dx=16y2∫x dx\int 16 x y^{2}\, dx = 16 y^{2} \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: 8x2y28 x^{2} y^{2}

    1. Don't know the steps in finding this integral.

      But the integral is

      log⁡(x)\log{\left(x \right)}

    The result is: 8x2y2+log⁡(x)8 x^{2} y^{2} + \log{\left(x \right)}

  2. Add the constant of integration:

    8x2y2+log⁡(x)+constant8 x^{2} y^{2} + \log{\left(x \right)}+ \mathrm{constant}

The answer is:

8x2y2+log⁡(x)+constant8 x^{2} y^{2} + \log{\left(x \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                         
 |                                          
 | /  1         2\             2  2         
 | |1*- + 16*x*y | dx = C + 8*x *y  + log(x)
 | \  x          /                          
 |                                          
/
8 x2 y2+log⁡x8\,x^2\,y^2+\log x
Simplify
The answer [src] 
        2
oo + 8*y
%a{\it \%a} 
=
= 
        2
oo + 8*y
8y2+∞8 y^{2} + \infty
Упростить

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

    © Mister Exam – Calculator