Question

Evaluate: ∫x(x³+3)dx

Answer 1

u need simplify it be : x(x³+3) = x^4+3x
now, integrate

Answer 2

it then become 4x³+3?

Answer 3

nvm I'm not suppose to derive right?

Answer 4

yes, that is derivative :)

Answer 5

what is n suppose to be then?

Answer 6

oh, u have remembered the basic formula before :
int (x^n) dx = 1/(n+1) x^(n+1)

look, u can divided 2 cases like this :
int (x^4+3x) dx = int x^4 dx + int 3x dx
just integrate one by one

Answer 7

so for int 3x dx, n is 1?

Answer 8

yup, or u can move the 3 to infront the sign of integral :
int (3x) dx = 3 int x dx

Answer 9

so, 3 as the coefficient... just find int x, then times 3

Answer 10

ok, so for the first int, I got:
\[\frac{ 1 }{ 5 }x ^{5}+C\]
For second int, I got:
\[3\int\limits_{}^{}\frac{ 1 }{ 2 }x ^{2}dx\]

Answer 11

+C along with the second int

Answer 12

is that correct?

Answer 13

for the 2nd, why still there is integral sign :)

Answer 14

I thought I have to put the 3 in front of the integral sign, so I left it

Answer 15

yes, after u have integrate... miss the sign integral, u have found its result

Answer 16

so it would be
\[3\frac{ 1 }{ 2 }x ^{2}dx\]?

Answer 17

just 3/2 x^2
dont use dx again :)

Answer 18

3 * 1/2 = 3/2

Answer 19

Do I have to add C like
\[\frac{ 3 }{ 2 }x^{2}+C\]?

Answer 20

yes, all solution is 1/5x^5 + 3/2x^2 + c

Answer 21

it is indefinite integrals, so always endly + c

Answer 22

ohh i see, Ty

Answer 23

your're welcome