en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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 (4x^3)/((x^4+7)^2)

\int \frac{4 x ^{3}}{( x ^{4} + 7 ) ^{2}} d x

integral of t^{(-1)/2}(t^2-t+2)

\int t^{\frac{- 1}{2}} (t^{2} - t + 2) d t

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 ln(5sqrt(x))

\int ln (5 x) d x

integral of-1/(3x^3)

\int - \frac{1}{3 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