Evaluate: int(1+2sinx/cos^2x)dx?
1 Answer
May 28, 2018
#I=tan(x)+2sec(x)+C#
Explanation:
I assume you want to integrate
#I=int(1+2sin(x))/(cos^2(x))dx#
Splitting into two terms
#I=int1/(cos^2(x))dx+int(2sin(x))/(cos^2(x))dx#
First integral
Remember
#I_1=int1/(cos^2(x))dx#
#color(white)(I)=intsec^2(x)dx#
#color(white)(I)=tan(x)+C_1#
Second integral
Make a substitution
#I_1=int(2sin(x))/(cos^2(x))dx#
#color(white)(I_1)=-2int1/u^2du larr color(red)("The substitution"#
#color(white)(I_1)=2/u+C_2#
#color(white)(I_1)=2/cos(x)+C_2#
#color(white)(I_1)=2sec(x)+C_2#
Combining these
#I=tan(x)+2sec(x)+C#