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Popular >

integral of t^2-3t+2

Solution

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

Solution

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

Solution steps

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

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

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

\int 2 d t = 2 t

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

Add a constant to the solution

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

Popular Examples

integral of 2x*x^2

\int 2 x \cdot x^{2} d x

integral of x/(sqrt(81-x^2))

\int \frac{x}{81 - x ^{2}} d x

integral of yx^3e^{x^2y^2}

\int y x^{3} e^{x^{2} y^{2}} d y

integral of x^3e^{-x/c}

\int x^{3} e^{- \frac{x}{c}} d x

integral of (sqrt(x)+3x)

\int (x + 3 x) d x

Frequently Asked Questions (FAQ)

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