7. Use integration by parts to prove that for any positive integer n, | cos"x dx = 1 cosn-1xx+ n - 1 " cosn-2x dx n

Q: Integrate S(cos x)e*+sin xdx B. et-sinx + C A. -e4+sin x + C c. e4+sinx + C D. e-4+sinx +C A В C D

A: Given: I=∫cosxe4+sinxdx  ....(1)   We know that; ∫eax+bdx=1aeax+b+C

Q: x sin wx dx x2 + 6x + 10 Show that (2 sin 3w – 3 cos 3w) w > 0 %3D - 2e2w

A:

Q: I-Shinx dx Ig-/sin'xdx 2-x2 dx

A: We have to evaluate the above integrals. NOTE - According to our guidelines we have to answer only…

Q: 3. (2 + ln x)³ √ (2+1) X A. (2 + ln x) 4 +C -dx C. (2 + Inx)³ + C 4 {1tinx? Syn (2+1mx) +C 20 B. (2…

A: We can solve the integral using substitution method. Here we substitute 2+lnx by z and then apply…

Q: 1. Show that cosh 4x = 8cosh“x - 8cosh? x + 1 .

A: Given problem:- Show that cosh(4x) = 8cosh4x - 8cosh2x + 1

Q: Integrate the square root of ( 1- cos x) dx O 2 sqrt(2) cos (1/2 x) + C O - 2 sqrt(2) cos x + C - 2…

A:

Q: X Evaluate the integral sin cos -dx. 2 4 X 2 X X [sin 4 cos dx = 2 2

A: Given indefinite integral ∫sin4x2cosx2dx

Q: ,2 Compute x² cos(x³ + 3) dx

A:

Q: Evaluate the following integral e* sin5x dx Select one: O( ex/26 ) ( sin5x - 5 cos5x) +C O( ex/26 )…

A: Given, Evaluate the following integral  ∫ex sin 5x dx   The required calculation can be defined by…

Q: T/2 / csc²x dx л/4 T/2 / (csc?x +o ´x + csc x cot x) dx T/2 csc x cot x dx

A:

Q: valuate f¹² Vsin x + 1 cos x dx.

A: Topic:- application of integration

Q: Evaluate COs 2 4 – x² dx

A: use the property of even function and odd function to evaluate the integral.

Q: xp sin 5x cos 3xt cos 5xsin 3x xp x²+ 2x + 5 EX Find:

A:

Q: Find So Cosx (x² + 1)² - ex

A: We shall be using basics of residue calculus to evaluate this integral

Q: Evaluate dx J x[(lnx)² + 9]

A:

Q: Use the double-angle formula cos 2x = 2 cos x – 1 to evaluate the integral 1 1+ cos 2x dx

A: The given integral is ∫11+cos2xdx