the exercise will be on file please

4. [-/0.16 Points] DETAILS SCALCET8 7.5.004. 0/100 Submissions Used Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) 3 sin ( x ) dx cos(x) Need Help? Read It 5. [-/0.16 Points] DETAILS SCALCET8 7.5.005. 0/100 Submissions Used Evaluate the integral. (Use C for the constant of integration.) 4 + 5 Need Help? Read It Watch It 6. [-/0.16 Points] DETAILS SCALCET8 7.5.007. 0/100 Submissions Used Evaluate the integral. gearctan(y) 1+ yz -dy Need Help? Read It Watch It2. [-/0.16 Points] DETAILS SCALCET8 7.5.AE.005. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Video Example () EXAMPLE 5 9 + x d Although the rationalizing substitution U = 9 - X 9 +x works here, it leads to a very complicated rational function. An easier method is to do some algebraic manipulation. Multiplying numerator and denominator by \\ 9 - x, we have V81 - 2 dx = /( Jax - / V 81 - x 2 dx + C . Need Help? Read It 3. [-/0.16 Points] DETAILS SCALCET8 7.5.AE.002. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Video Example .() EXAMPLE 2 ev 8x dx According to (ii) in Step 3(d), we substitute u = v 8x. Then 8x = so dx = du and evexax = ue" du. The integrand is now a product of u and the transcendental function e" so it can be integrated by parts. Choosing U = U dv' = e du du' = du we have ev 8 x x A / M el du Le" + C Lev 8x + C.1. [-/0.16 Points] DETAILS SCALCET8 7.5.AE.004. 0/100 Submissions Used Video Example () EXAMPLE 4 dx XV In(7x) We substitute u = In(7x) because its differential is du = dx, which occurs in the integral. We have dx x In(7x) = Vudu = du 20 + c = 2 (In(7x) ) + C Need Help? Read It