What is the integral of y/(sqrt(4+y^2)) ?

The integral of y/(sqrt(4+y^2)) is sqrt(4+y^2)+C

Popular >

integral of y/(sqrt(4+y^2))

\int \frac{y}{4 + y ^{2}} d y

4 + y^{2} + C

Solution steps

\int \frac{y}{4 + y ^{2}} d y

Apply u-substitution

: \int \frac{1}{2 u} d u

= \int \frac{1}{2 u} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Apply the Power Rule

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

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

Substitute back

u = 4 + y^{2}

= \frac{1}{2} \cdot 2 (4 + y^{2})^{\frac{1}{2}}

Simplify

\frac{1}{2} \cdot 2 (4 + y^{2})^{\frac{1}{2}} : 4 + y^{2}

= 4 + y^{2}

Add a constant to the solution

= 4 + y^{2} + C

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

\int \frac{2}{x} ln (x) d x

\int \frac{tan ( t )}{sin ( 2 t )} d t

\int sec^{8} (3 x) tan (3 x) d x

\int + (2 a x + b) (a x^{2} + b x)^{7} d x

What is the integral of y/(sqrt(4+y^2)) ?
The integral of y/(sqrt(4+y^2)) is sqrt(4+y^2)+C