What is the integral of e^t+2t+ln(t) ?

The integral of e^t+2t+ln(t) is e^t+t^2+tln(t)-t+C

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integral of e^t+2t+ln(t)

\int e^{t} + 2 t + ln (t) d t

e^{t} + t^{2} + t ln (t) - t + C

Solution steps

\int e^{t} + 2 t + ln (t) d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int e^{t} d t + \int 2 t d t + \int ln (t) d t

\int e^{t} d t = e^{t}

\int 2 t d t = t^{2}

\int ln (t) d t = t ln (t) - t

= e^{t} + t^{2} + t ln (t) - t

Add a constant to the solution

= e^{t} + t^{2} + t ln (t) - t + C

\int \frac{1}{x ^{2} + 2 x - 8} d x

\frac{d}{d x} (- sin (2 x) \cdot 2)

\int \frac{1}{x ^{2} \cdot 5 + x ^{2}} d x

y^{^{''}} - 8 y^{^{'}} + 18 y = 0, y (0) = - 4, y^{^{'}} (0) = 3

\int \frac{( 1 - cos ( 2 x ) )}{2} d x

What is the integral of e^t+2t+ln(t) ?
The integral of e^t+2t+ln(t) is e^t+t^2+tln(t)-t+C