en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 4x^3+5

Solution

\int 4 x^{3} + 5 d x

Solution

x^{4} + 5 x + C

Solution steps

\int 4 x^{3} + 5 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 4 x^{3} d x + \int 5 d x

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

\int 5 d x = 5 x

= x^{4} + 5 x

Add a constant to the solution

= x^{4} + 5 x + C

Popular Examples

integral of (x+3)/((x^2+6x)^3)

\int \frac{x + 3}{( x ^{2} + 6 x ) ^{3}} d x

integral of (6(x+1))/(sqrt(2x+1))

\int \frac{6 ( x + 1 )}{2 x + 1} d x

integral of e^x(5-2e^x)^2

\int e^{x} (5 - 2 e^{x})^{2} d x

integral of ((x^2-3x+8))/((x^2-4x+7)^2)

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

integral of sqrt(200+200cos(x))

\int 200 + 200 cos (x) d x

Frequently Asked Questions (FAQ)

What is the integral of 4x^3+5 ?
The integral of 4x^3+5 is x^4+5x+C