What is the integral of x^2+2cos(x)+3 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^2+2cos(x)+3

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

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

Solution steps

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

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

\int 2 cos (x) d x = 2 sin (x)

\int 3 d x = 3 x

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

Add a constant to the solution

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

\int \frac{5 x ^{2} - 7 x + 10}{x ^{3} + 12 x ^{2} + 36 x} d x

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

\int \frac{1}{2 t ^{2}} d t

\int (\frac{arctan ( 3 x )}{1 + 9 x ^{2}}) d x

\int 9 x x^{2} + 1 d x

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