Evaluate (2x^2 + 1 / x^3) dx?

Question

Determine (2x^2 + 1 / x^3) dx show step by step work

(a) -2/3 x^3 - 1/2x^2 + C

(b) -2/3 x^3 + 1/2x^2 + C

(c) 2/3 x^3 - 1/2x^2 + C

(d) 2/3 x^3 + 1/2x^2 + C

Answer 1

First you integrate each one separately:
integration of a fuction of x occurs by adding one to the power of x and dividing this function by the number that the exponent holds:
2x^2 dx = 2 (x^2+1)/(2+1) = 2/3 x^3
1/(x^3) dx = (x^-3) dx = (x^-3+1)/(-3+1) = (x^-2)/ -2 = -1/2x^2

( 2x^2 + 1(x^-3) ) dx = { (2/3)(x^3) +( 1/-2)(x^-2) +c}

= 2/3 x^3 -1/2x^2 +c which is answer C

Answer 2

You didn't say you wanted to intergrate it.

⌠(2x²) + (1/ x^3) dx
Intergrate by parts:
= ⌠2x²) + (x^-3) dx
= 2/3(x^3) + (x-²/-2) + c
= 2/3(x^3) - (x-²/2) + c
= 2/3(x^3) - 1/2x² + c
That is, Answer c.

Answer 3

(2x^2 + 1 / x^3)
=(2x^2 + x^-3) , because 1/a = a^-1

Integral (2x^2 + x^-3) dx
(2/3)x^3 - (1/2)(x^-2) + C

or C

Answer 4

wahh can't you just do your own work yourself?

[okay i'm assuming you're doing integration here.]

right.

so S (2 x^2 + x ^ -3 ) dx
= [2 x ^ (2+1)] / (2+1) + [x ^ (-3 + 1)]/ (-3 + 1) + c
= ( 2 x^3 ) / 3 - 1 / (2 x^2) + c

Answer 5

(x^3 + 2x^2 + 3x - 6) = (x - one million) (x^2 + 3x + 6) you do not favor lengthy branch btw, in basic terms factorise. speedier and a lot less stressful! had to strive against with my a aspect instructor to be able to do it this kind.