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Popular Calculus >

integral of t^2-t+6

Solution

\int t^{2} - t + 6 d t

Solution

\frac{t ^{3}}{3} - \frac{t ^{2}}{2} + 6 t + C

Solution steps

\int t^{2} - t + 6 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 t d t + \int 6 d t

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

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

\int 6 d t = 6 t

= \frac{t ^{3}}{3} - \frac{t ^{2}}{2} + 6 t

Add a constant to the solution

= \frac{t ^{3}}{3} - \frac{t ^{2}}{2} + 6 t + C

Graph

Popular Examples

integral of (8x+10)/((x^2-2x+2)^{3/2)}

\int \frac{8 x + 10}{( x ^{2} - 2 x + 2 ) ^{\frac{3}{2}}} d x

integral of (-4x)/((x+1)-sqrt(x+1))

\int \frac{- 4 x}{( x + 1 ) - x + 1} d x

integral of (1-cos^2(x))^2

\int (1 - cos^{2} (x))^{2} d x

integral of ((csc^2(x)))/(cot^3(x))

\int \frac{( csc ^{2} ( x ) )}{cot ^{3} ( x )} d x

integral of (3x-2)/(5x^2-3x+8)

\int \frac{3 x - 2}{5 x ^{2} - 3 x + 8} d x

Frequently Asked Questions (FAQ)

What is the integral of t^2-t+6 ?
The integral of t^2-t+6 is (t^3)/3-(t^2)/2+6t+C