What is (x+sqrt(x^2+1))^2 ?

The solution to (x+sqrt(x^2+1))^2 is 2x^2+2xsqrt(x^2+1)+1

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simplify (x+sqrt(x^2+1))^2

simplify

(x + x^{2} + 1)^{2}

2 x^{2} + 2 x x^{2} + 1 + 1

Solution steps

(x + x^{2} + 1)^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(x + x^{2} + 1)^{2} = x^{2} + 2 x x^{2} + 1 + (x^{2} + 1)^{2}

= x^{2} + 2 x x^{2} + 1 + (x^{2} + 1)^{2}

Simplify

x^{2} + 2 x x^{2} + 1 + (x^{2} + 1)^{2} : 2 x^{2} + 2 x x^{2} + 1 + 1

= 2 x^{2} + 2 x x^{2} + 1 + 1

(1 + cos^{2} (x)) (tan (x))

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

\frac{2 e ^{- s}}{s ( s + 1 )}

(1 + \frac{2}{3} x)^{8} (3 + 8 x)^{2}

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

What is (x+sqrt(x^2+1))^2 ?
The solution to (x+sqrt(x^2+1))^2 is 2x^2+2xsqrt(x^2+1)+1