What is the integral of xsec^2(x^2) ?

The integral of xsec^2(x^2) is 1/2 tan(x^2)+C

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integral of xsec^2(x^2)

\int x sec^{2} (x^{2}) d x

\frac{1}{2} tan (x^{2}) + C

Solution steps

\int x sec^{2} (x^{2}) d x

Apply u-substitution

: \int \frac{sec ^{2} ( u )}{2} d u

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

Take the constant out:

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

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

Use the common integral:

\int sec^{2} (u) d u = tan (u)

= \frac{1}{2} tan (u)

Substitute back

u = x^{2}

= \frac{1}{2} tan (x^{2})

Add a constant to the solution

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

n = 0 \sum \infty (\frac{1}{5})^{n}

12 arcsin (e^{\frac{x}{2}})

\frac{7 x}{8}

\frac{d y}{d x} + 5 y = 0, y (0) = 2

f (x) = x^{3} - 4 x + 6, at x = 2

What is the integral of xsec^2(x^2) ?
The integral of xsec^2(x^2) is 1/2 tan(x^2)+C