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Popular >

integral of t^2-4t+8

Solution

\int t^{2} - 4 t + 8 d t

Solution

\frac{t ^{3}}{3} - 2 t^{2} + 8 t + C

Solution steps

\int t^{2} - 4 t + 8 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 4 t d t + \int 8 d t

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

\int 4 t d t = 2 t^{2}

\int 8 d t = 8 t

= \frac{t ^{3}}{3} - 2 t^{2} + 8 t

Add a constant to the solution

= \frac{t ^{3}}{3} - 2 t^{2} + 8 t + C

Popular Examples

limit as t approaches 2-of (t+2)/(t^2-4)

t \to 2 - lim (\frac{t + 2}{t ^{2} - 4})

integral of (9x^2-8x+4)

\int (9 x^{2} - 8 x + 4) d x

sum from n=1 to infinity of 8(1/5)^n

n = 1 \sum \infty 8 (\frac{1}{5})^{n}

derivative of (5x^{7x})

\frac{d}{d x} ((5 x)^{7 x})

limit as x approaches 0+of (5x)/(sin(x))

x \to 0 + lim (\frac{5 x}{sin ( x )})

Frequently Asked Questions (FAQ)

What is the integral of t^2-4t+8 ?
The integral of t^2-4t+8 is (t^3)/3-2t^2+8t+C