What is the integral of x*sec^2(x) ?

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

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integral of x*sec^2(x)

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

x tan (x) + ln ∣ cos (x) ∣ + C

Solution steps

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

Apply Integration By Parts

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

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

\int tan (x) d x = - ln ∣ cos (x) ∣

= x tan (x) - (- ln ∣ cos (x) ∣)

Simplify

= x tan (x) + ln ∣ cos (x) ∣

Add a constant to the solution

= x tan (x) + ln ∣ cos (x) ∣ + C

\frac{\partial}{\partial x} (\frac{x + 4}{y + 1})

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

\int cos^{3} (1) d x

f (x) = (3 x + 2) (4 x^{2} + 3)

\frac{\partial}{\partial x} (ln (x^{3} + y^{2}))

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