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

The integral of (xsin(x))/((cos(x))^2) is xsec(x)-ln|tan(x)+sec(x)|+C

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

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

x sec (x) - ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

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

Rewrite using trig identities

= \int x sec (x) tan (x) d x

Apply Integration By Parts

= x sec (x) - \int sec (x) d x

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

= x sec (x) - ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= x sec (x) - ln ∣ tan (x) + sec (x) ∣ + C

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

x \to 2 lim (x^{2} - 5)

x \to 0 lim (\frac{1 - e ^{- x}}{x})

\frac{d}{d x} (\frac{x ^{2}}{x ^{3}})

d er i v a t i v e e^{x} (x^{2} + 1) (x + 4)

What is the integral of (xsin(x))/((cos(x))^2) ?
The integral of (xsin(x))/((cos(x))^2) is xsec(x)-ln|tan(x)+sec(x)|+C