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

The integral of 2xsec^2(x) is 2(xtan(x)+ln|cos(x)|)+C

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integral of 2xsec^2(x)

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

2 (x tan (x) + ln ∣ cos (x) ∣) + C

Solution steps

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

Apply Integration By Parts

: x tan (x) - \int tan (x) d x

= 2 (x tan (x) - \int tan (x) d x)

\int tan (x) d x = - ln ∣ cos (x) ∣

= 2 (x tan (x) - (- ln ∣ cos (x) ∣))

Simplify

= 2 (x tan (x) + ln ∣ cos (x) ∣)

Add a constant to the solution

= 2 (x tan (x) + ln ∣ cos (x) ∣) + C

\frac{d}{d x} (x ln (10 x))

\int \frac{( 2 x - 1 ) e ^{x^{2}}}{e ^{x}} d x

f (t) = 1 \cdot t^{3}

\frac{d}{d x} (x + lo g_{e} (x))

x^{2} - x

What is the integral of 2xsec^2(x) ?
The integral of 2xsec^2(x) is 2(xtan(x)+ln|cos(x)|)+C