What is the integral of x/(cos^2(x^2)) ?

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

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integral of x/(cos^2(x^2))

\int \frac{x}{cos ^{2} ( x ^{2} )} d x

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

Solution steps

\int \frac{x}{cos ^{2} ( x ^{2} )} d x

Apply u-substitution

: \int \frac{1}{2 cos ^{2} ( u )} d u

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

Use the common integral:

\int \frac{1}{cos ^{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

\int x^{2} sin (x z) d z

x \to 0 lim (\frac{x + 2 - 2}{2 x + 5 - 3})

\int cos (x) \cdot sin^{3} (x) d x

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

y^{^{'}} = 135 y x^{4}

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