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
The integral of ∫1/(1+tanx)dx can be found by using a trigonometric identity and substitution. The result is ∫1/(1+tanx)dx = x - arctan(tan(x)/2) + C, where C is the constant of integration.
A useful substitution to solve this integral is u = tan(x/2). This substitution simplifies the integral because it transforms the tangent function into a rational function, making it easier to integrate.
Using the substitution u = tan(x/2), we can express tan(x) in terms of u, which helps in rewriting the integral in a simpler form. This substitution leads to the differential dx = 2du/(1+u^2), and the integral becomes easier to handle.
Trigonometric identities play a crucial role in simplifying the integrand. For example, using the identity tan(x) = 2tan(x/2)/(1-tan^2(x/2)), we can rewrite the integral in a form that is more straightforward to integrate.
No, the integral ∫1/(1+tanx)dx is not typically solved using partial fractions. Instead, it is more effectively solved using trigonometric identities and substitution methods, such as the substitution u = tan(x/2).