What is the integral of e^{-t(s+5)} ?

The integral of e^{-t(s+5)} is e^{-(5+s)t}t-(-5-s) 1/((-5-s)^2)(-e^{-t(5+s)}t(5+s)-e^{-t(5+s)})+C

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integral of e^{-t(s+5)}

\int e^{- t (s + 5)} d t

e^{- (5 + s) t} t - (- 5 - s) \frac{1}{( - 5 - s ) ^{2}} (- e^{- t (5 + s)} t (5 + s) - e^{- t (5 + s)}) + C

Solution steps

\int e^{- t (s + 5)} d t

Apply Integration By Parts

: e^{- (5 + s) t} t - \int e^{- (5 + s) t} (- 5 - s) t d t

= e^{- (5 + s) t} t - \int e^{- (5 + s) t} (- 5 - s) t d t

\int e^{- (5 + s) t} (- 5 - s) t d t = (- 5 - s) \frac{1}{( - 5 - s ) ^{2}} (- e^{- t (5 + s)} t (5 + s) - e^{- t (5 + s)})

= e^{- (5 + s) t} t - (- 5 - s) \frac{1}{( - 5 - s ) ^{2}} (- e^{- t (5 + s)} t (5 + s) - e^{- t (5 + s)})

Add a constant to the solution

= e^{- (5 + s) t} t - (- 5 - s) \frac{1}{( - 5 - s ) ^{2}} (- e^{- t (5 + s)} t (5 + s) - e^{- t (5 + s)}) + C

e^{2 x}, 2

\frac{\partial}{\partial z} (e^{x y} ln (z))

f (x) = 2 x^{3} + 5 x^{2}, at x = - 2

\frac{d}{d x} (\frac{a x + 1 + x}{x ^{2} - 1})

\frac{\partial}{\partial x} (2 x^{2} y e^{x} + 2)

What is the integral of e^{-t(s+5)} ?
The integral of e^{-t(s+5)} is e^{-(5+s)t}t-(-5-s) 1/((-5-s)^2)(-e^{-t(5+s)}t(5+s)-e^{-t(5+s)})+C