What is the integral of 20xsec^2(x) ?

The integral of 20xsec^2(x) is 20(xtan(x)+ln|cos(x)|)+C

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integral of 20xsec^2(x)

\int 20 x sec^{2} (x) d x

20 (x tan (x) + ln ∣ cos (x) ∣) + C

Solution steps

\int 20 x sec^{2} (x) d x

Take the constant out:

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

= 20 \cdot \int x sec^{2} (x) d x

Apply Integration By Parts

= 20 (x tan (x) - \int tan (x) d x)

\int tan (x) d x = - ln ∣ cos (x) ∣

= 20 (x tan (x) - (- ln ∣ cos (x) ∣))

Simplify

= 20 (x tan (x) + ln ∣ cos (x) ∣)

Add a constant to the solution

= 20 (x tan (x) + ln ∣ cos (x) ∣) + C

\int \frac{1}{x \cdot x - 1} d x

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

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

\frac{\partial}{\partial x} (2 x + 2 y)

\frac{\partial}{\partial x} (9 x + y + 7 x y)

What is the integral of 20xsec^2(x) ?
The integral of 20xsec^2(x) is 20(xtan(x)+ln|cos(x)|)+C