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Popular >

integral of t(t^3-1)

Solution

\int t (t^{3} - 1) d t

Solution

\frac{t ^{5}}{5} - \frac{t ^{2}}{2} + C

Solution steps

\int t (t^{3} - 1) d t

Expand

t (t^{3} - 1) : t^{4} - t

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

\int t^{4} d t = \frac{t ^{5}}{5}

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

= \frac{t ^{5}}{5} - \frac{t ^{2}}{2}

Add a constant to the solution

= \frac{t ^{5}}{5} - \frac{t ^{2}}{2} + C

Graph

Popular Examples

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\frac{d}{d x} (\frac{e ^{x} + cos ( x )}{x ^{2}})

3 y^{^{'}} = 2 y

integral of (x^2)/(sqrt(25+x^2))

\int \frac{x ^{2}}{25 + x ^{2}} d x

derivative of 7x^4-2x^3+8x+5

\frac{d}{d x} (7 x^{4} - 2 x^{3} + 8 x + 5)

limit as x approaches 0 of e^{2x}-1

x \to 0 lim (e^{2 x} - 1)

Frequently Asked Questions (FAQ)

What is the integral of t(t^3-1) ?
The integral of t(t^3-1) is (t^5)/5-(t^2)/2+C