What is the integral of x^2sech^2(x^3) ?

The integral of x^2sech^2(x^3) is 1/3 tanh(x^3)+C

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integral of x^2sech^2(x^3)

\int x^{2} sech^{2} (x^{3}) d x

\frac{1}{3} tanh (x^{3}) + C

Solution steps

\int x^{2} sech^{2} (x^{3}) d x

Apply u-substitution

: \int \frac{u sech ^{2} ( u ^{\frac{3}{2}} )}{2 x} d u

= \int \frac{sech ^{2} ( u )}{3} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int sech^{2} (u) d u

Use the common integral:

\int sech^{2} (u) d u = tanh (u)

= \frac{1}{3} tanh (u)

Substitute back

u = x^{3}

= \frac{1}{3} tanh (x^{3})

Add a constant to the solution

= \frac{1}{3} tanh (x^{3}) + C

\frac{d}{d x} (x^{3} - 8)

y^{^{'}} + 2 y = 25 sin (x) + 40 cos (x), y (0) = 1

y = x, (9, 3)

n = 6 \sum \infty \frac{5 ^{n}}{1 2 ^{n}}

3 y^{^{''}} + 17 y^{^{'}} - 6 y = 0

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