What is the integral from 0 to x of (t^3+3t^2+2) ?

The integral from 0 to x of (t^3+3t^2+2) is (x^4)/4+x^3+2x

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integral from 0 to x of (t^3+3t^2+2)

\int_{0}^{x} (t^{3} + 3 t^{2} + 2) d t

\frac{x ^{4}}{4} + x^{3} + 2 x

Solution steps

\int_{0}^{x} t^{3} + 3 t^{2} + 2 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_{0}^{x} t^{3} d t + \int_{0}^{x} 3 t^{2} d t + \int_{0}^{x} 2 d t

\int_{0}^{x} t^{3} d t = \frac{x ^{4}}{4}

\int_{0}^{x} 3 t^{2} d t = x^{3}

\int_{0}^{x} 2 d t = 2 x

= \frac{x ^{4}}{4} + x^{3} + 2 x

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\int_{3}^{7} x^{3} d x

\int_{\frac{x}{2}}^{3 - x} x + y d y

What is the integral from 0 to x of (t^3+3t^2+2) ?
The integral from 0 to x of (t^3+3t^2+2) is (x^4)/4+x^3+2x