Question

for my homework it says use symbolic integration utiltiy to find the indefinite integral...
whats that mean?

Answer 1

The term symbolic is used to distinguish this problem from that of numerical integration, where the value of F at a particular input or set of inputs, rather than a general formula for F, is sought.

Answer 2

in general , it just mean "indefinite integral"

Answer 3

do you have an example of the problem?

Answer 4

find the indefinite integral of x^3/(1-x^4)^(1/2)

Answer 5

\[ \int\limits_{}{x} ^{3}/\sqrt{1-x^{4}} dx\]

Answer 6

substitution:
u=1-x^4
then du=-4*x^3 dx

try it

Answer 7

whats that suppose to be?

Answer 8

x^3 dx =1/4 du

right?

Answer 9

i did it

Answer 10

i got -1/2(1-x^4)^1/2 +C

Answer 11

sorry i didnt respont i was looking throug my notes

Answer 12

\[=-1/4 \int\limits_{ }^{}du/u ^{1/2}=-1/4 * 2/3 * u ^{3/2}=\]

Answer 13

yes i did that

Answer 14

=-1/6 (1-x^4) ^3/2 + const

Answer 15

its not 3/2 because its -1/2

Answer 16

oups... you are right!

Answer 17

the square root was originally to the bottom sorry if i didnt make it clear

Answer 18

thank you ! your help is greatly appreciated :)

Answer 19

so I got:
-1/2 (1-x^4)^1/2 + const
right?

Answer 20

:)

Answer 21

okay lol