What is the integral of (5t^3+2t^2+t) ?

The integral of (5t^3+2t^2+t) is (5t^4)/4+(2t^3)/3+(t^2)/2+C

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integral of (5t^3+2t^2+t)

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

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

Solution steps

\int 5 t^{3} + 2 t^{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 5 t^{3} d t + \int 2 t^{2} d t + \int t d t

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

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

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

= \frac{5 t ^{4}}{4} + \frac{2 t ^{3}}{3} + \frac{t ^{2}}{2}

Add a constant to the solution

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

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What is the integral of (5t^3+2t^2+t) ?
The integral of (5t^3+2t^2+t) is (5t^4)/4+(2t^3)/3+(t^2)/2+C