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Ab L.

asked • 09/16/16

What is the integral of t^5/v(t^2+7) dt ?

I got an answer but not sure about it. Thanks.

2 Answers By Expert Tutors

By:

Ben K. answered • 09/16/16

Tutor
4.9 (223)

JHU Grad specializing in Math and Science

Mark M.

tutor
Just thought of an easier way which avoids the trig substitution stuff: Let u = t2+7  Then du = 2tdt and t2 = u-7
 
So, the integral can be written as ∫t4/√(t2+7)tdt
 
=∫(u-7)2/(√u)(1/2)du
 
=(1/2)∫(u- 14u + 49)/√udu
 
= (1/2)∫[u3/2 -14u1/2 + 49u-1/2] + C
 
= (1/5)u5/2 - (14/3)u3/2 + 49u1/2 + C 
 
= (1/5)(t2+7)5/2 - (14/3)(t2+7)3/2 + 49(t2+7)1/2 + C
 
Mark M (Bayport, NY)
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09/16/16

Ben K.

Yup. Mark has the alternate solution, here.
Report

09/16/16

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