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Popular >

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

Popular Examples

integral of (x^2+x+1)/((x+1)^{50)}

\int \frac{x ^{2} + x + 1}{( x + 1 ) ^{50}} d x

integral of (2x+5)/(x^2+3x-10)

\int \frac{2 x + 5}{x ^{2} + 3 x - 10} d x

integral of 1/(x^{1/2)-x^{1/3}}

\int \frac{1}{x ^{\frac{1}{2}} - x ^{\frac{1}{3}}} d x

integral of (2x-3)/(x^2+8x+7)

\int \frac{2 x - 3}{x ^{2} + 8 x + 7} d x

integral of (x+1)(x-3)

\int (x + 1) (x - 3) 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