What is the integral of 3x+cos(x) ?

The integral of 3x+cos(x) is (3x^2)/2+sin(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 3x+cos(x)

\int 3 x + cos (x) d x

\frac{3 x ^{2}}{2} + sin (x) + C

Solution steps

\int 3 x + cos (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 3 x d x + \int cos (x) d x

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

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

= \frac{3 x ^{2}}{2} + sin (x)

Add a constant to the solution

= \frac{3 x ^{2}}{2} + sin (x) + C

\int (3 x + 1) sin (x) d x

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

\int cos^{\frac{3}{2}} (x) sin^{3} (x) d x

\int e^{l n (x^{2} + 1)} d x

\int - \frac{1}{x ln ( x )} d x

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