What is the integral of (sqrt((u^2)^{22)})/(1+(u^2)^{22)}u^2)^2 ?

The integral of (sqrt((u^2)^{22)})/(1+(u^2)^{22)}u^2)^2 is (u^{104})/(u^{176)+1}+C

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integral of (sqrt((u^2)^{22)})/(1+(u^2)^{22)}u^2)^2

\int \frac{( ( ( u ^{2} ) ^{2} ) ^{2} ) ^{22}}{1 + ( ( ( u ^{2} ) ^{2} ) ^{2} ) ^{22}} d (((u^{2})^{2})^{2})^{2}

\frac{u ^{104}}{u ^{176} + 1} + C

Solution steps

\int \frac{( ( ( u ^{2} ) ^{2} ) ^{2} ) ^{22}}{1 + ( ( ( u ^{2} ) ^{2} ) ^{2} ) ^{22}} d (((u^{2})^{2})^{2})^{2}

Integral of a constant:

\int a d x = a x

= \frac{( ( ( u ^{2} ) ^{2} ) ^{2} ) ^{22}}{( ( ( u ^{2} ) ^{2} ) ^{2} ) ^{22} + 1} (((u^{2})^{2})^{2})^{2}

Simplify

\frac{( ( ( u ^{2} ) ^{2} ) ^{2} ) ^{22}}{( ( ( u ^{2} ) ^{2} ) ^{2} ) ^{22} + 1} (((u^{2})^{2})^{2})^{2} : \frac{u ^{104}}{u ^{176} + 1}

= \frac{u ^{104}}{u ^{176} + 1}

Add a constant to the solution

= \frac{u ^{104}}{u ^{176} + 1} + C

x^{6} + y^{5} x^{7} + 3 y^{^{'}} = 0, y (0) = 0

\frac{d x}{d y} = 2 x - 5 x + 1

\int_{0}^{\infty} 2 e^{- x} d x

y^{^{'}} = \frac{y}{2} + 4 e^{\frac{t}{2}}

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

What is the integral of (sqrt((u^2)^{22)})/(1+(u^2)^{22)}u^2)^2 ?
The integral of (sqrt((u^2)^{22)})/(1+(u^2)^{22)}u^2)^2 is (u^{104})/(u^{176)+1}+C