en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ax^4+bx^3+3c

Solution

\int a x^{4} + b x^{3} + 3 c d x

Solution

\frac{a x ^{5}}{5} + \frac{b x ^{4}}{4} + 3 c x + C

Solution steps

\int a x^{4} + b x^{3} + 3 c d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int a x^{4} d x + \int b x^{3} d x + \int 3 c d x

\int a x^{4} d x = \frac{a x ^{5}}{5}

\int b x^{3} d x = \frac{b x ^{4}}{4}

\int 3 c d x = 3 c x

= \frac{a x ^{5}}{5} + \frac{b x ^{4}}{4} + 3 c x

Add a constant to the solution

= \frac{a x ^{5}}{5} + \frac{b x ^{4}}{4} + 3 c x + C

Popular Examples

integral of x/(x^4-2x^3+2x^2-2x+1)

\int \frac{x}{x ^{4} - 2 x ^{3} + 2 x ^{2} - 2 x + 1} d x

integral of (5^y+(6x)/(y+4))

\int (5^{y} + \frac{6 x}{y + 4}) d x

integral of 10x^{-1}

\int 10 x^{- 1} d x

integral of (sin(x))^4(cos(x))^6

\int (sin (x))^{4} (cos (x))^{6} d x

integral of-10t^2+9

\int - 10 t^{2} + 9 d t

Frequently Asked Questions (FAQ)

What is the integral of ax^4+bx^3+3c ?
The integral of ax^4+bx^3+3c is (ax^5)/5+(bx^4)/4+3cx+C