Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) \int37e^{74x}\arctan(e^{37x})dx Inverse Trigonometric Forms (92): \int u\tan^{-1}u\ du=\frac{u^{2}+1}{2}\tan^{-1}u-\frac{u}{2}+C

Nann 2021-05-14 Answered
Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.)
37e74xarctan(e37x)dx
Inverse Trigonometric Forms (92): utan1u du=u2+12tan1uu2+C
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Expert Answer

curwyrm
Answered 2021-05-15 Author has 87 answers

Step 1
(37)e74xtan1(e37x)dx
e37x=t(37)e37xdx=dt=ttan1(t)dt
From table given formula number 92:
utan1udu=u2+12tan1uu2+C
t2+12tan1tt2+C
e74x+12tan1(e37x)e37x2+C

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