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

解答

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

\frac{x ^{16}}{x ^{176} + 1} + C

求解步骤

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

常数积分:

\int a d x = a x

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

化简

\frac{1}{( ( ( x ^{2} ) ^{2} ) ^{2} ) ^{22} + 1} (((x^{2})^{2})^{2})^{2} : \frac{x ^{16}}{x ^{176} + 1}

= \frac{x ^{16}}{x ^{176} + 1}

解答补常数

= \frac{x ^{16}}{x ^{176} + 1} + C

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