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

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

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integral of (x+x^3)/(sqrt(1+2x^2+x^4))

\int \frac{x + x ^{3}}{1 + 2 x ^{2} + x ^{4}} d x

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

Solution steps

\int \frac{x + x ^{3}}{1 + 2 x ^{2} + x ^{4}} d x

Simplify

\frac{x + x ^{3}}{1 + 2 x ^{2} + x ^{4}} : x

= \int x d x

Apply the Power Rule

= \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{2}}{2} + C

\int \frac{sin ^{2} ( \frac{x}{2} )}{sin ^{2} ( x )} d x

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

\int \frac{1}{x ( ln ( x ^{2} ) ) ^{6}} d x

\int \frac{5 x ^{2} + 1}{x - 1} d x

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

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