What is the integral of sqrt(e^{3t)}-1/(2sqrt(t)) ?

The integral of sqrt(e^{3t)}-1/(2sqrt(t)) is 2/3 e^{(3t)/2}-sqrt(t)+C

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integral of sqrt(e^{3t)}-1/(2sqrt(t))

\int e^{3 t} - \frac{1}{2 t} d t

\frac{2}{3} e^{\frac{3 t}{2}} - t + C

Solution steps

\int e^{3 t} - \frac{1}{2 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^{3 t} d t - \int \frac{1}{2 t} d t

\int e^{3 t} d t = \frac{2}{3} e^{\frac{3 t}{2}}

\int \frac{1}{2 t} d t = t

= \frac{2}{3} e^{\frac{3 t}{2}} - t

Add a constant to the solution

= \frac{2}{3} e^{\frac{3 t}{2}} - t + C

(3.6) (10.12)

\int t sec^{2} (2 t) d t

\int \frac{5 ( x ^{2} + 3 )}{x ( x ^{2} + 5 )} d x

(sin (t))^{2}

\int 2 t \cdot (- cos (2 t)) d t

What is the integral of sqrt(e^{3t)}-1/(2sqrt(t)) ?
The integral of sqrt(e^{3t)}-1/(2sqrt(t)) is 2/3 e^{(3t)/2}-sqrt(t)+C