What is the integral of (x^2-sin(x)) ?

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

\int (x^{2} - sin (x)) d x

\frac{x ^{3}}{3} + cos (x) + C

Solution steps

\int x^{2} - 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 x^{2} d x - \int sin (x) d x

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

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

= \frac{x ^{3}}{3} - (- cos (x))

Simplify

= \frac{x ^{3}}{3} + cos (x)

Add a constant to the solution

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

\int x^{4} 10 + x^{5} d x

\int (x + 3)^{7} d x

\int \frac{5}{7 x} d x

\int \frac{x}{225 x ^{2} - 1} d x

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

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