In the following equation/s, find the indefinite integral . \int t^{3}\sqrt{t^{4}+1}dt

Emeli Hagan

Emeli Hagan

Answered question

2021-06-04

In the following equation/s, find the indefinite integral .
t3t4+1dt

Answer & Explanation

l1koV

l1koV

Skilled2021-06-05Added 100 answers

Step 1
Given:
t2t3+1dt
Step 2
t3t4+1dt
Apply u−substitution method
u=t4+1
du=4t3dt
du4=t3dt
Then the integral becomes,
=udu4
=14(u12+112+1)
=14(u3232)+C
u=t4+1back
=14((t4+1)3232)+C
=16(t4+1)32+C
t3t4+132+C
t3t4+1dt=16(t4+1)32+C
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-24Added 2605 answers

Answer is given below (on video)

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