Tiêu đề Integration-1 & Biotechnology- Daily-14 (Set-A)-With Solve.pdf ✅

4 e ̈vL ̈v:  x 1 – x 2 dx = – 1 2  – 2x 1 – x 2 dx = – 1 2  d(1 – x 2 ) 1 – x 2 = – 1 2  2 1 – x 2 + c = – 1 – x 2 + c 21.  sinx dx = KZ? cosx + c – cosx + c – 180  cosx + c 180  cosx + c DËi: – 180  cosx + c e ̈vL ̈v:  sin x 180 dx     1 =  180 = – cos x 180  180 = – 180  cosx + c Note:  sinax dx = – cosax a + c 22.  dx x 2 – 3x + 2 = ? ln(x – 2) – ln(x – 1) ln(x – 2) + ln(x – 1) ln(x + 2) – ln(x + 1) ln(x + 2) + ln(x + 1) DËi: ln(x – 2) – ln(x – 1) e ̈vL ̈v:  dx x 2 – 3x + 2 =  dx x 2 – 2x – x + 2 =  dx (x – 2)(x – 1) =      1 x – 2 – 1 x – 1 dx [Thumb Rule cÖ‡qvM K‡i] = ln(x – 2) – ln(x – 1) + c 23.  dx (3sinx – 5cosx) 2 = ? 1 9tanx + 15 + c 1 3tanx – 5 + c 1 15 – 9tanx + c None DËi: 1 15 – 9tanx + c e ̈vL ̈v:  dx (3sinx – 5cosx) 2 =  sec2 x (3tanx – 5) 2 dx [je I ni‡K sec2 x Øviv ̧Y K‡i] =  1 (3z – 5) 2 dz = 1 3  – 1 3z – 5 + c awi, z = tanx  dz = sec2 x dx = 1 15 – 9tanx + c 24.  dx (x – 3)(x – 4) = ? 1 2 ln x 2 – 7x + 12 + c 2ln| (x – 3) + x – 4| + c ln x – 3 x – 4 + c None DËi: 2ln| (x – 3) + x – 4| + c e ̈vL ̈v: Shortcut:  dx (x – a) (x – b) = 2ln | x – a + x – b| + c 25.  dx x 2 + 4x + 5 = ? tan–1 (x + 2) + c 2tan–1 (x + 4) + c cos–1 (x + 5) + c tan–1 (x + 3) + c DËi: tan–1 (x + 2) + c e ̈vL ̈v:  dx x 2 + 4x + 5 =  dx x 2 + 4x + 1 + 4 =  dx (x + 2) 2 + 1 = tan–1 (x + 2) + c 26.  1 18  2x2 dx = KZ? 1 2 sin1x 3 + c 1 3 2 tan1 x 3 + c 1 6 2 ln     3 + x 3  x + c 1 2 sin1 x 3 + c DËi: 1 2 sin1x 3 + c e ̈vL ̈v:  1 18  2x2 dx = 1 2(9  x 2 ) dx = 1 2  dx 3 2  x 2 = 1 2 sin1 x 3 + c 27.  e x . 5x dx = ? e x ln5 1 + ln5 + c e x (1 + ln5) + c e x (1 + ln5) ln5 + c e x(1 + ln5) 1 + ln5 + c DËi: e x(1 + ln5) 1 + ln5 + c e ̈vL ̈v:  e x .5x dx =  e x e ln5x dx =  e x(1 + ln5) dx = e x(1 + ln5) 1 + ln5 + c