What is the integral of (9x^2)/2-5cos(x)+7 ?

The integral of (9x^2)/2-5cos(x)+7 is (3x^3)/2-5sin(x)+7x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (9x^2)/2-5cos(x)+7

\int \frac{9 x ^{2}}{2} - 5 cos (x) + 7 d x

\frac{3 x ^{3}}{2} - 5 sin (x) + 7 x + C

Solution steps

\int \frac{9 x ^{2}}{2} - 5 cos (x) + 7 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 \frac{9 x ^{2}}{2} d x - \int 5 cos (x) d x + \int 7 d x

\int \frac{9 x ^{2}}{2} d x = \frac{3 x ^{3}}{2}

\int 5 cos (x) d x = 5 sin (x)

\int 7 d x = 7 x

= \frac{3 x ^{3}}{2} - 5 sin (x) + 7 x

Add a constant to the solution

= \frac{3 x ^{3}}{2} - 5 sin (x) + 7 x + C

What is the integral of (9x^2)/2-5cos(x)+7 ?
The integral of (9x^2)/2-5cos(x)+7 is (3x^3)/2-5sin(x)+7x+C