What is the integral of 5sqrt(4x-3) ?

The integral of 5sqrt(4x-3) is 5/6 (4x-3)^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5sqrt(4x-3)

\int 5 4 x - 3 d x

\frac{5}{6} (4 x - 3)^{\frac{3}{2}} + C

Solution steps

\int 5 4 x - 3 d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int 4 x - 3 d x

Apply u-substitution

: \int \frac{u}{4} d u

= 5 \cdot \int \frac{u}{4} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \frac{1}{4} \cdot \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= 5 \cdot \frac{1}{4} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 4 x - 3

= 5 \cdot \frac{1}{4} \cdot \frac{2}{3} (4 x - 3)^{\frac{3}{2}}

Simplify

5 \cdot \frac{1}{4} \cdot \frac{2}{3} (4 x - 3)^{\frac{3}{2}} : \frac{5}{6} (4 x - 3)^{\frac{3}{2}}

= \frac{5}{6} (4 x - 3)^{\frac{3}{2}}

Add a constant to the solution

= \frac{5}{6} (4 x - 3)^{\frac{3}{2}} + C

\int \frac{1}{81 - 49 x ^{2}} d x

\int 7 x^{2} (x^{3} - 8)^{19} d x

\int (\frac{x ^{2}}{3} - 8 x - 3) d x

\int sin^{5} (x) cos^{9} (x) d x

\int 16 x^{4} - 24 x^{2} + 9 d x

What is the integral of 5sqrt(4x-3) ?
The integral of 5sqrt(4x-3) is 5/6 (4x-3)^{3/2}+C