What is the integral of 5x+sin(x) ?

The integral of 5x+sin(x) is (5x^2)/2-cos(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5x+sin(x)

\int 5 x + sin (x) d x

\frac{5 x ^{2}}{2} - cos (x) + C

Solution steps

\int 5 x + sin (x) 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 5 x d x + \int sin (x) d x

\int 5 x d x = \frac{5 x ^{2}}{2}

\int sin (x) d x = - cos (x)

= \frac{5 x ^{2}}{2} - cos (x)

Add a constant to the solution

= \frac{5 x ^{2}}{2} - cos (x) + C

x \to - 4 lim (x + 4)

(y + 4) (\frac{d y}{d x}) = 2 x y + 4 y

\frac{d y}{d x} = 4 x e^{2 y}

\frac{1}{c}

f (x) = tan (x) + x, at x = \frac{π}{4}

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