What is the integral of (e^t-\sqrt[4]{16t}+3/(t^3)) ?

The integral of (e^t-\sqrt[4]{16t}+3/(t^3)) is e^t-8/5 t^{5/4}-3/(2t^2)+C

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integral of (e^t-\sqrt[4]{16t}+3/(t^3))

e^{t} - \frac{8}{5} t^{\frac{5}{4}} - \frac{3}{2 t ^{2}} + C

Solution steps

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 = e^{t}

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

= e^{t} - \frac{8}{5} t^{\frac{5}{4}} - \frac{3}{2 t ^{2}}

Add a constant to the solution

= e^{t} - \frac{8}{5} t^{\frac{5}{4}} - \frac{3}{2 t ^{2}} + C

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

g (x) = x^{2}, [0, 1]

x \to \infty lim (4 x - 1)

\int_{0}^{l n (3)} \frac{e ^{t}}{e ^{2 t} + 49} d t

\frac{d y}{d x} = cos^{2} (y)

What is the integral of (e^t-\sqrt[4]{16t}+3/(t^3)) ?
The integral of (e^t-\sqrt[4]{16t}+3/(t^3)) is e^t-8/5 t^{5/4}-3/(2t^2)+C