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

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

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

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

x tan (x) + ln ∣ cos (x) ∣ + C

Solution steps

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

\int \frac{16 x ^{2}}{9 - 4 x ^{2}} d x

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\int 4 x^{5} e^{x} d x

\int \frac{x ^{4} + x}{x} d x

cos (x^{2})

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