en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3x+5

Solution

\int 3 x + 5 d x

Solution

\frac{3 x ^{2}}{2} + 5 x + C

Solution steps

\int 3 x + 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 3 x d x + \int 5 d x

\int 3 x d x = \frac{3 x ^{2}}{2}

\int 5 d x = 5 x

= \frac{3 x ^{2}}{2} + 5 x

Add a constant to the solution

= \frac{3 x ^{2}}{2} + 5 x + C

Popular Examples

derivative of 2cos(x-sin(2x))

\frac{d}{d x} (2 cos (x) - sin (2 x))

y^'= x/(200)-y/(100)

y^{^{'}} = \frac{x}{200} - \frac{y}{100}

derivative of 1/3 x^3-5/2 x^2+6x+1

\frac{d}{d x} (\frac{1}{3} x^{3} - \frac{5}{2} x^{2} + 6 x + 1)

integral of-1/x*1/x

\int - \frac{1}{x} \cdot \frac{1}{x} d x

derivative of f(x)=sqrt(x-1)derivative of

f (x) = x - 1

Frequently Asked Questions (FAQ)

What is the integral of 3x+5 ?
The integral of 3x+5 is (3x^2)/2+5x+C