Please show us. Thanks.Rhdjfgjgj said:Homework Statement: my teacher told me to solve this one in all the possible ways . I seem to have missed out on any one of them. Please help me oout
Relevant Equations: All standard integrals and concepts covered in AP calculus
I have done one by assuming tanx as u in substitution
To find the integral of ∫1/(1+tanx)dx, we can use the substitution method. Let u = tan(x), then du = sec^2(x)dx. After substituting, the integral becomes ∫1/(1+u) * du, which is a standard integral that can be easily solved.
Yes, you can simplify the integrand before finding the integral. In this case, you can rewrite tan(x) as sin(x)/cos(x) and then simplify the expression to 1/(1+sin(x)/cos(x)). This will make it easier to integrate.
Yes, there are alternative methods to find the integral of ∫1/(1+tanx)dx. You can use trigonometric identities to simplify the integrand further or use partial fractions to break down the expression into simpler terms.
Yes, there is a specific range of values for x where this integral is valid. Since tan(x) is not defined at odd multiples of π/2 (x = (2n+1)π/2), the integral ∫1/(1+tanx)dx is valid for all x except these values.
Yes, you can use online tools or software like Wolfram Alpha or Symbolab to calculate the integral of ∫1/(1+tanx)dx. These tools can provide step-by-step solutions and help you understand the process of finding the integral.