Question

how do you work out the integral of 4t^3 times squareroot(1+9t^4)dt

Answer 1

try a substitution of a trig function

Answer 2

a trig function? l dont follow

Answer 3

As,
\[\int\limits4t^3*\sqrt{1+9t^4} dt=1/9(\int\limits36t^3*\sqrt{1+9t^4} dt)=1/9*{(1+9t^4)^{3/2}}/(3/2)\]

Answer 4

then \[2/27*(1+9t^4)^{3/2}+c \]

Answer 5

Sorry , a little bit messy :(

Answer 6

Got my way or not

Answer 7

@Muhammad Nauman Umair
some of your steps are missing because of the usage of equation...

Answer 8

the steps which i skipped are not difficult to understand @callisto

Answer 9

oh thanx guys that was really helpful

Answer 10

welcome