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Popular >

integral of (t^3-9t)

Solution

\int (t^{3} - 9 t) d t

Solution

\frac{t ^{4}}{4} - \frac{9 t ^{2}}{2} + C

Solution steps

\int t^{3} - 9 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^{3} d t - \int 9 t d t

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

\int 9 t d t = \frac{9 t ^{2}}{2}

= \frac{t ^{4}}{4} - \frac{9 t ^{2}}{2}

Add a constant to the solution

= \frac{t ^{4}}{4} - \frac{9 t ^{2}}{2} + C

Popular Examples

(\partial)/(\partial x)((t+1)/(t-1))

\frac{\partial}{\partial x} (\frac{t + 1}{t - 1})

(d^4)/(dx^4)(cos(x^2))

\frac{d ^{4}}{d x ^{4}} (cos (x^{2}))

integral from-2 to 2 of |2x^2-2x|

\int_{- 2}^{2} 2 x^{2} - 2 x d x

integral from 0 to x of f(t)

\int_{0}^{x} f (t) d t

f(x)= 3/(1+x^2)

f (x) = \frac{3}{1 + x ^{2}}

Frequently Asked Questions (FAQ)

What is the integral of (t^3-9t) ?
The integral of (t^3-9t) is (t^4)/4-(9t^2)/2+C