What is the integral of 1/(sqrt(3-4x)) ?

The integral of 1/(sqrt(3-4x)) is -1/2 sqrt(3-4x)+C

Popular >

integral of 1/(sqrt(3-4x))

\int \frac{1}{3 - 4 x} d x

- \frac{1}{2} 3 - 4 x + C

Solution steps

\int \frac{1}{3 - 4 x} d x

Apply u-substitution

: \int - \frac{1}{4 u} d u

= \int - \frac{1}{4 u} d u

Take the constant out:

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

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

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= - \frac{1}{4} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 3 - 4 x

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

Simplify

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

= - \frac{1}{2} 3 - 4 x

Add a constant to the solution

= - \frac{1}{2} 3 - 4 x + C

\int \frac{2021}{x ^{4} + 1} d x

\int sec^{2} (7 θ) d θ

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

\int \frac{1}{10 - x ^{2}} d x

\int 4 sin (x) + cos (x) d x

What is the integral of 1/(sqrt(3-4x)) ?
The integral of 1/(sqrt(3-4x)) is -1/2 sqrt(3-4x)+C