How to to integrate.?

Question

Can one please help me with intergrating the equation below.

2/3 X^2 + 3/4 X ^4

Pleeeeeaaaaassseeeee!!!!!

Answer 1

sure its pretty easy.

you add one to the 2 in the square of the x and divide by 3. in the next one you add one to 4 and divide by 5.

so

2/3 * 1/3 x^3 + 3/4 * 1/5 x^5

2/9x^3 + 3/20x^5

Answer 2

Remember the reverse power rule:
If x doesn't equal -1, then ∫ x^n dx = x^(n+1)/(n+1) +C
Also, constants can be taken outside the integral sign.
So, your answer is
2/3*x³/3 + 3/4x^5/5 + C,
which simplifies to
2/9x³ + 3/20 x^5+ C.

Answer 3

∫{(2/3)x^2 + (3/4)x^4}dx = (1/3)(2/3)x^3 + (1/5)(3/4)x^5 + C
= (2/9)x^3 + (3/20)x^5 + C

Answer 4

∫[(2/3) X^2 + (3/4) X ^4]dx =
(2/9)X^3 + (3/20)X^5 + C

Answer 5

The simplest polynom whose derivative is 2/3 X^2 is 2/9 X^3
The simplest polynom whose derivative is 3/4 X^4 is 3/20 X^5
the adjective simplest meaning that each term can have a constant number added to it.
Now, it's your job to put a plus sign between both. Think it's feasible enough, is it not?

Answer 6

yes:
(2/3)*(1/3) X^3 + (3/4)*(1/5)* X ^5
which becomes
2/9 X^3 + 3/16 X ^5

Answer 7

answer is
2/9x^3+3/20x^5