Question

determine integral: S t^3/2t^4 -5 dt

Answer 1

S t^3/2t^4 -5 dt =
S t^3/2t^4 + S -5 dt =
1/2 S t^3/t^4 - 5 t =
1/2 S 1/t - 5t =
1/2 * ln t - 5 t + C

Answer 2

\[\int\limits \frac{t^3}{2t^4-5}dt\]
Let u=2t^4-5
then du=8t^3 dt
So:(1/8)du=t^3dt
So your integral becomes:
\[\frac{1}{8} \int\limits \frac{du}{u}=\frac{1}{8}\ln|u|+C=\frac{1}{8}\ln|2t^4-5|+C\]
Note: If the "-5" is NOT in the denominator of the fraction. Then Ana2's method is correct.

Answer 3

yeah it is in the denominator of the fraction

Answer 4

Then my method would be the appropriate one :)

Answer 5

ok how do u know to do 1/8?

Answer 6

Because you have 8t^3 but in the numerator you only have t^3. In other words, its off by a factor of 8. So you need to divide by 8.