Match the statements of Column I with values of Column II Column IColumn II(A) ∫e2x−2exe2x+1dx=A ln(e2x+1)+B tan−1(ex)+c(p) A=−12, B=−14(B) ∫√x+√x2+2dx=A{x+√x2+2}32+B√x+√x2+2+c(q) A=12, B=−2(C) ∫cos 8x−cos 7x1+2 cos 5xdx=A sin 3x+B sin 2x+c(r) A=13, B=−2(D) ∫ln xx3dx=Aln xx2+Bx2+c(s) A=13, B=−12

Match the statements of Column I with values of Column II Column IColu

1.	Match the statements of Column I with values of Column II Column IColumn II(A) ∫e2x−2exe2x+1dx=A ln(e2x+1)+B tan−1(ex)+c(p) A=−12, B=−14(B) ∫√x+√x2+2dx=A{x+√x2+2}32+B√x+√x2+2+c(q) A=12, B=−2(C) ∫cos 8x−cos 7x1+2 cos 5xdx=A sin 3x+B sin 2x+c(r) A=13, B=−2(D) ∫ln xx3dx=Aln xx2+Bx2+c(s) A=13, B=−12
Answer» Match the statements of Column I with values of Column II $\begin{matrix} C o l u m n I & C o l u m n I I (A) \int \frac{e^{2 x} - 2 e^{x}}{e^{2 x} + 1} d x = A l n (e^{2 x} + 1) + B t a n^{- 1} (e^{x}) + c & (p) A = - \frac{1}{2}, B = - \frac{1}{4} (B) \int \sqrt{x + \sqrt{x^{2} + 2}} d x = A {x + \sqrt{x^{2} + 2}}^{\frac{3}{2}} + \frac{B}{\sqrt{x + \sqrt{x^{2} + 2}}} + c & (q) A = \frac{1}{2}, B = - 2 (C) \int \frac{c o s 8 x - c o s 7 x}{1 + 2 c o s 5 x} d x = A s i n 3 x + B s i n 2 x + c & (r) A = \frac{1}{3}, B = - 2 (D) \int \frac{l n x}{x^{3}} d x = A \frac{l n x}{x^{2}} + \frac{B}{x^{2}} + c & (s) A = \frac{1}{3}, B = - \frac{1}{2} \end{matrix}$