Question

anyone can help me to evaluate this integrals

Answer 1

\[\int\limits_{}^{}(z+3)^4dz\]

Answer 2

@eliassaab @Owlcoffee

Answer 3

to integrate, you have to add 1 to your exponent which would make it 5. however, as you can see, its derivative makes it so that there is no constant which means that the integral has a denominator of 5 as well.

Answer 4

can i expand the formula then integrate?

Answer 5

if you expand it, it would be much more difficult

Answer 6

i got \[\frac{ \left( z+3 \right)^5 }{ 5 }\]

Answer 7

but im not so sure about it

Answer 8

that is correct :)

Answer 9

are you sure about it?

Answer 10

yes

Answer 11

therefore its the same process for this problem?\[\int\limits_{}^{}(4x+1)^2dx\]

Answer 12

not quite, this is one would be easier when expanded

Answer 13

but can i apply the same process on the previous problem?

Answer 14

yes and no, in a way you could, but it's just difficult since you also would have to integrate the inside

Answer 15

so is it possible if i put it this way?\[= \frac{ 1 }{ 3 }(4x+1)^3\]

Answer 16

differentiate your answer

if your answer is correct, you should get back the integrand

Answer 17

whats the derivative of \(\frac{ 1 }{ 3 }(4x+1)^3\) ?

Answer 18

@Saitama which part u didn't understand?

Answer 19

(4x+1)^2 is the derivative

Answer 20

ha?

Answer 21

treat the (z+3) as a single variable, say u so that \(u = (z+3); du = dz\)
\[\int u^4 du \]

Answer 22

i dont use u-substitution?

Answer 23

so what are you allowed to do?

Answer 24

simplest and easiest unless you have not been taught about this yet

Answer 25

can i solve it w/o u-substitution?

Answer 26

try

Answer 27

1/5(z+3)^5 +c

Answer 28

how on earth did you come up with that?

Answer 29

+1 to the exponent and on denominator put the new exponent?

Answer 30

am i right @eliassaab

Answer 31

whats the real answer to this, im confused please show me...

Answer 32

whats the derivative of \(\frac{ 1 }{ 3 }(4x+1)^3\) ?

Earlier you have replied :

`(4x+1)^2 is the derivative`

Answer 33

that is wrong, don't you know the chain rule ?

Answer 34

derivative of \(x^n\) with respect to \(x\) is indeed \(n*x^{n-1}\).
But we don't have just the \(x\) in above example right ?

Answer 35

I think that you got it right
\[\int (z+3)^4 \, dz=\frac{1}{5} (z+3)^5 + C\]

Answer 36

i think only by sustitution u solve these type of integrals...

Answer 37

coz here there is a function inside a function...it is like..f(g(x)) so u have to take g(x)=t for reducing it to f(t)..so that you can solve it easily..