The following improper integral arises in the study of certain damped oscillatory motion, such as that of a pendulum that eventually comes to rest due to friction: $\int_{0}^{\infty} e^{-t}(1+\cos t) d t$ .
If this integral converges, give an upper bound for it.If not, enter "DNC".

Question

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The Answer of The following improper integral arises in the study of certain damped oscillatory motion, such as that of a pendulum that eventually comes to rest due to friction: $\int_{0}^{\infty} e^{-t}(1+\cos t) d t$ .
If this integral converges, give an upper bound for it.If not, enter "DNC".

The Following Improper Integral Arises in the Study of Certain ∫0∞e−t(1+cos⁡t)dt\int_{0}^{\infty} e^{-t}(1+\cos t) d t∫0∞​e−t(1+cost)dt

The Following Improper Integral Arises in the Study of Certain $\int_{0}^{\infty} e^{-t}(1+\cos t) d t$