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Popular >

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

Solution

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

Solution

\frac{1}{4} ln 2 x^{2} + 2 + C

Solution steps

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{4} ln ∣ u ∣

Substitute back

u = 2 x^{2} + 2

= \frac{1}{4} ln 2 x^{2} + 2

Add a constant to the solution

= \frac{1}{4} ln 2 x^{2} + 2 + C

Popular Examples

integral of (x^{1.6}+11x^{4.5})

\int (x^{1.6} + 11 x^{4.5}) d x

integral of 1/(cos(x)+3)

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

integral of ln(2x^2+1)

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

integral of (x-1)^7(x+1)

\int (x - 1)^{7} (x + 1) d x

integral of xcos(x^2+4)sqrt(sin(x^2+4))

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

Frequently Asked Questions (FAQ)

What is the integral of x/(2x^2+2) ?
The integral of x/(2x^2+2) is 1/4 ln|2x^2+2|+C