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Popular Calculus >

integral of 3t^3-t

Solution

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

Solution

\frac{3 t ^{4}}{4} - \frac{t ^{2}}{2} + C

Solution steps

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

\int 3 t^{3} d t = \frac{3 t ^{4}}{4}

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

= \frac{3 t ^{4}}{4} - \frac{t ^{2}}{2}

Add a constant to the solution

= \frac{3 t ^{4}}{4} - \frac{t ^{2}}{2} + C

Graph

Popular Examples

integral of (2x^2-3x-3)/(x^3-3x^2+7x-5)

\int \frac{2 x ^{2} - 3 x - 3}{x ^{3} - 3 x ^{2} + 7 x - 5} d x

integral of 3/((1+x^2))

\int \frac{3}{( 1 + x ^{2} )} d x

integral of sin(4)

\int sin (4) d x

integral of 1/(9x+2)

\int \frac{1}{9 x + 2} d x

integral of x*tan(x/3)

\int x \cdot tan (\frac{x}{3}) d x

Frequently Asked Questions (FAQ)

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