What is the integral of 2xsec^2(4x^2) ?

The integral of 2xsec^2(4x^2) is 1/4 tan(4x^2)+C

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integral of 2xsec^2(4x^2)

\int 2 x sec^{2} (4 x^{2}) d x

\frac{1}{4} tan (4 x^{2}) + C

Solution steps

\int 2 x sec^{2} (4 x^{2}) d x

Take the constant out:

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

= 2 \cdot \int x sec^{2} (4 x^{2}) d x

Apply u-substitution

: \int \frac{sec ^{2} ( u )}{8} d u

= 2 \cdot \int \frac{sec ^{2} ( u )}{8} d u

Take the constant out:

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

= 2 \cdot \frac{1}{8} \cdot \int sec^{2} (u) d u

Use the common integral:

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

= 2 \cdot \frac{1}{8} tan (u)

Substitute back

u = 4 x^{2}

= 2 \cdot \frac{1}{8} tan (4 x^{2})

Simplify

2 \cdot \frac{1}{8} tan (4 x^{2}) : \frac{1}{4} tan (4 x^{2})

= \frac{1}{4} tan (4 x^{2})

Add a constant to the solution

= \frac{1}{4} tan (4 x^{2}) + C

x \to (\frac{π}{2}) + lim (x - \frac{π}{2})

\frac{d}{d x} (4 x^{2} y + 2 z^{3})

x \to 0 lim ((tan (x))^{x})

f (x) = 1 - e^{c o s (1 - x^{2})}

e^{e - 3 x}

What is the integral of 2xsec^2(4x^2) ?
The integral of 2xsec^2(4x^2) is 1/4 tan(4x^2)+C