What is the integral of x[cosh^2(2x^2)-sinh^2(2x^2)] ?

The integral of x[cosh^2(2x^2)-sinh^2(2x^2)] is (x^2)/2+C

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integral of x[cosh^2(2x^2)-sinh^2(2x^2)]

\int x [cosh^{2} (2 x^{2}) - sinh^{2} (2 x^{2})] d x

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

Solution steps

\int x [cosh^{2} (2 x^{2}) - sinh^{2} (2 x^{2})] d x

Simplify

x [cosh^{2} (2 x^{2}) - sinh^{2} (2 x^{2})] : x

= \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

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

Add a constant to the solution

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

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What is the integral of x[cosh^2(2x^2)-sinh^2(2x^2)] ?
The integral of x[cosh^2(2x^2)-sinh^2(2x^2)] is (x^2)/2+C