What is the integral of (tan(x))' ?

The integral of (tan(x))' is x(tan(x))'-xtan^2(x)-x+tan(x)+C

Popular >

integral of (tan(x))'

\int (tan (x))^{'} d x

x (tan (x))' - x tan^{2} (x) - x + tan (x) + C

Solution steps

\int (tan (x))^{'} d x

Apply Integration By Parts

: (tan (x))^{'} x - \int 2 sec^{2} (x) tan (x) x d x

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

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

= (tan (x))^{^{'}} x - (x tan^{2} (x) + x - tan (x))

Simplify

(tan (x))^{'} x - (x tan^{2} (x) + x - tan (x)) : x (tan (x))^{'} - x tan^{2} (x) - x + tan (x)

= x (tan (x))^{'} - x tan^{2} (x) - x + tan (x)

Add a constant to the solution

= x (tan (x))^{^{'}} - x tan^{2} (x) - x + tan (x) + C

\int ln (x) arcsin (x) d x

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

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

\int cos^{4} (θ) sin (2 θ) d θ

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

What is the integral of (tan(x))' ?
The integral of (tan(x))' is x(tan(x))'-xtan^2(x)-x+tan(x)+C