What is the integral of 5x^{3/2}+2sqrt(x)-7x+3 ?

The integral of 5x^{3/2}+2sqrt(x)-7x+3 is 2x^{5/2}+4/3 x^{3/2}-(7x^2)/2+3x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5x^{3/2}+2sqrt(x)-7x+3

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

2 x^{\frac{5}{2}} + \frac{4}{3} x^{\frac{3}{2}} - \frac{7 x ^{2}}{2} + 3 x + C

Solution steps

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

\int 5 x^{\frac{3}{2}} d x = 2 x^{\frac{5}{2}}

\int 2 x d x = \frac{4}{3} x^{\frac{3}{2}}

\int 7 x d x = \frac{7 x ^{2}}{2}

\int 3 d x = 3 x

= 2 x^{\frac{5}{2}} + \frac{4}{3} x^{\frac{3}{2}} - \frac{7 x ^{2}}{2} + 3 x

Add a constant to the solution

= 2 x^{\frac{5}{2}} + \frac{4}{3} x^{\frac{3}{2}} - \frac{7 x ^{2}}{2} + 3 x + C

\int \frac{x}{u} d u

\int \frac{3 x ^{2} - 2 x + 7}{x ^{2} - 3 x + 2} d x

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

\int - 14 x sin (7 x^{2} - 1) d x

sin (2 t)

What is the integral of 5x^{3/2}+2sqrt(x)-7x+3 ?
The integral of 5x^{3/2}+2sqrt(x)-7x+3 is 2x^{5/2}+4/3 x^{3/2}-(7x^2)/2+3x+C