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Popular >

integral of y/(y^2+3)

Solution

\int \frac{y}{y ^{2} + 3} d y

Solution

\frac{1}{2} ln y^{2} + 3 + C

Solution steps

\int \frac{y}{y ^{2} + 3} 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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

Substitute back

u = y^{2} + 3

= \frac{1}{2} ln y^{2} + 3

Add a constant to the solution

= \frac{1}{2} ln y^{2} + 3 + C

Popular Examples

integral of x^2 1/(1+x^2)

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

integral of (ln((3+x^2)^x))/(3+x^2)

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

integral of 4xcos^2(x)

\int 4 x cos^{2} (x) d x

integral of 1/((x+1)^{2/3)}

\int \frac{1}{( x + 1 ) ^{\frac{2}{3}}} d x

integral of ((2x+1))/(x^3-7x+6)

\int \frac{( 2 x + 1 )}{x ^{3} - 7 x + 6} d x

Frequently Asked Questions (FAQ)

What is the integral of y/(y^2+3) ?
The integral of y/(y^2+3) is 1/2 ln|y^2+3|+C