What is the integral of 4x^3+sin(x) ?

The integral of 4x^3+sin(x) is x^4-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 4x^3+sin(x)

\int 4 x^{3} + sin (x) d x

x^{4} - cos (x) + C

Solution steps

\int 4 x^{3} + 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 4 x^{3} d x + \int sin (x) d x

\int 4 x^{3} d x = x^{4}

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

= x^{4} - cos (x)

Add a constant to the solution

= x^{4} - cos (x) + C

\int \frac{3 x ^{3} - x ^{2} + 6 x + 24}{x ^{2} - 2 x + 5} d x

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

\int \frac{e ^{4 x}}{( 1 + 3 e ^{4 x} ) ^{2}} d x

\int e^{\frac{y}{x + y}} d x

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

What is the integral of 4x^3+sin(x) ?
The integral of 4x^3+sin(x) is x^4-cos(x)+C