What is the integral of (t^4+5t^3+4) ?

The integral of (t^4+5t^3+4) is (t^5)/5+(5t^4)/4+4t+C

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integral of (t^4+5t^3+4)

\int (t^{4} + 5 t^{3} + 4) d t

\frac{t ^{5}}{5} + \frac{5 t ^{4}}{4} + 4 t + C

Solution steps

\int t^{4} + 5 t^{3} + 4 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 t^{4} d t + \int 5 t^{3} d t + \int 4 d t

\int t^{4} d t = \frac{t ^{5}}{5}

\int 5 t^{3} d t = \frac{5 t ^{4}}{4}

\int 4 d t = 4 t

= \frac{t ^{5}}{5} + \frac{5 t ^{4}}{4} + 4 t

Add a constant to the solution

= \frac{t ^{5}}{5} + \frac{5 t ^{4}}{4} + 4 t + C

\frac{\partial}{\partial x} (sin (- 2 x) cos (2 y))

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

f (x) = e^{x} \cdot cos (x), at x = 0

\int z^{m} d z

\frac{1}{1 - x}, 0

What is the integral of (t^4+5t^3+4) ?
The integral of (t^4+5t^3+4) is (t^5)/5+(5t^4)/4+4t+C