What is the integral of 4/3 t^3-4t^2+3t+10 ?

The integral of 4/3 t^3-4t^2+3t+10 is (t^4)/3-(4t^3)/3+(3t^2)/2+10t+C

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integral of 4/3 t^3-4t^2+3t+10

\int \frac{4}{3} t^{3} - 4 t^{2} + 3 t + 10 d t

\frac{t ^{4}}{3} - \frac{4 t ^{3}}{3} + \frac{3 t ^{2}}{2} + 10 t + C

Solution steps

\int \frac{4}{3} t^{3} - 4 t^{2} + 3 t + 10 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 \frac{4}{3} t^{3} d t - \int 4 t^{2} d t + \int 3 t d t + \int 10 d t

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

\int 4 t^{2} d t = \frac{4 t ^{3}}{3}

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

\int 10 d t = 10 t

= \frac{t ^{4}}{3} - \frac{4 t ^{3}}{3} + \frac{3 t ^{2}}{2} + 10 t

Add a constant to the solution

= \frac{t ^{4}}{3} - \frac{4 t ^{3}}{3} + \frac{3 t ^{2}}{2} + 10 t + C

\frac{d}{d t} (t + 1)

x \to 5 + lim (\frac{2}{x ^{2} - 25})

cos (a^{8} + x^{8})

x \to 0 lim (\frac{x + 36 - 6}{x})

\frac{- x ^{2}}{y ^{2}}

What is the integral of 4/3 t^3-4t^2+3t+10 ?
The integral of 4/3 t^3-4t^2+3t+10 is (t^4)/3-(4t^3)/3+(3t^2)/2+10t+C