can anyone solves this? integrate square root of {1+x^4+2x^2}?

Answer 1

sqrt(1+x^4+2x^2) = sqrt(1+x^2)^2 =1 + x^2

inetgral = x + x^3/3 + C where C constant of integration

Answer 2

Integral ( sqrt(1 + x^4 + 2x^2) dx )

Rearrange and complete the square.

Integral ( sqrt(x^4 + 2x^2 + 1) dx )

Integral ( sqrt( (x^2 + 1)^2 ) dx )

Square root of a square is itself.

Integral ( (x^2 + 1) dx )

And now it's trivial.

(1/3)x^3 + x + C

Answer 3

once you have a concern like this: 2x² - 35 = 15 the 1st situation you do is attempt to split as many numbers from x as is possible. In math, the final rule in fixing an equation is that even if you do to a minimum of one component you do to the different besides so i circulate to characteristic 35 to the two facets to make it disappear on one component: 2x² - 35 + 35 = 15 + 35 which provides: 2x² = 50 In my quest to split x from all numbers i'm going to now divide the two facets by potential of two: 2x²/2= 50/2 which provides: x² = 25 i'm going to now locate the sq. root of the two facets: ?x² = ?25 x = +5 or - 5 (extremely some anybody is tempted to basically write down 5 yet you may desire to bear in mind that -5 * -5 is likewise 25)

Answer 4

1+x^4+2x^2 = (1+x^2)^2

Integral of sqrt(1+x^4+2x^2)

=integral of (1+x^2)

= (x + (x^3/3) + c)

= (1/3)x^3 + x + c

Answer 5

x^4 + 2x^2 +1 = (x^2 + 1)^2
So you need only integrate x^2 + 1.
You don't need absolute value because x^2 + 1 is always positive.

Answer 6

thats a simple one dude... u can use the Texas calculator of u are really not sure with integration and other mathematical stuff.