What is the integral of (sqrt(2x)+sin(3x)) ?

The integral of (sqrt(2x)+sin(3x)) is sqrt(2)xsqrt(x)-(sqrt(2))/3 x^{3/2}-1/3 cos(3x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (sqrt(2x)+sin(3x))

\int (2 x + sin (3 x)) d x

2 x x - \frac{2}{3} x^{\frac{3}{2}} - \frac{1}{3} cos (3 x) + C

Solution steps

\int 2 x + sin (3 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 2 x d x + \int sin (3 x) d x

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

\int sin (3 x) d x = - \frac{1}{3} cos (3 x)

= 2 x x - \frac{2}{3} x^{\frac{3}{2}} - \frac{1}{3} cos (3 x)

Add a constant to the solution

= 2 x x - \frac{2}{3} x^{\frac{3}{2}} - \frac{1}{3} cos (3 x) + C

\int p^{2} e^{p^{3}} d p

\int \frac{( x + 5 )}{x ^{2} - 8 x} d x

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

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

\int (2 x + 5) 4^{x^{2} + 5 x + 1} d x

What is the integral of (sqrt(2x)+sin(3x)) ?
The integral of (sqrt(2x)+sin(3x)) is sqrt(2)xsqrt(x)-(sqrt(2))/3 x^{3/2}-1/3 cos(3x)+C