What is the integral of 21xsec^2(x) ?

The integral of 21xsec^2(x) is 21(xtan(x)+ln|cos(x)|)+C

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integral of 21xsec^2(x)

\int 21 x sec^{2} (x) d x

21 (x tan (x) + ln ∣ cos (x) ∣) + C

Solution steps

\int 21 x sec^{2} (x) d x

Take the constant out:

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

= 21 \cdot \int x sec^{2} (x) d x

Apply Integration By Parts

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

= 21 (x tan (x) - \int tan (x) d x)

\int tan (x) d x = - ln ∣ cos (x) ∣

= 21 (x tan (x) - (- ln ∣ cos (x) ∣))

Simplify

= 21 (x tan (x) + ln ∣ cos (x) ∣)

Add a constant to the solution

= 21 (x tan (x) + ln ∣ cos (x) ∣) + C

\int \frac{1}{x ln ( x ) ln ( ln ( x ) )} d x

f (x) = 1 1^{x}

\frac{\partial}{\partial x} (\frac{x + y + z}{3})

x \to 2 - lim (\frac{1}{x})

\frac{d}{d x} (\frac{2 - x}{x ^{2} + 4})

What is the integral of 21xsec^2(x) ?
The integral of 21xsec^2(x) is 21(xtan(x)+ln|cos(x)|)+C