What is the integral of 5(sec(x))^2 ?

The integral of 5(sec(x))^2 is 5tan(x)+C

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integral of 5(sec(x))^2

\int 5 (sec (x))^{2} d x

5 tan (x) + C

Solution steps

\int 5 (sec (x))^{2} d x

Take the constant out:

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

= 5 \cdot \int (sec (x))^{2} d x

Simplify

= 5 \cdot \int sec^{2} (x) d x

Use the common integral:

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

= 5 tan (x)

Add a constant to the solution

= 5 tan (x) + C

y = \frac{4}{3} (2 x - 1)^{3}

x^{2} + 16

y = 2 x^{3} - x^{2} + 2

\int x^{3} (x^{2} - 1)^{7} d x

\int \frac{( x ^{3} )}{1 - 2 x ^{2}} d x