Question

(1) Evaluate
+5
Vx+ 5 + 9x
dx.​

Answer 1

Answer:

Step-by-step explanation:

Put (3x+5)=t so that 3dx=dt or dx=13dt.

∴ ∫(3x+5)7dx=13t7dt=13⋅t88+(3x+5)824+C.

(ii) Put (4−9x)=t so that−9dx=dtordx=−19dt.

∴∫(4−9x)5dx=−19∫t5dt=−19⋅t66+C−(4−9x)654+C.

(iii) Put (2−3x)=t so that−3dx=dt or dx=−13dt.

∴∫1(2−3x)4dx=−13∫1t4dt=−13⋅1−3t3+C=19(2−3x)3+C.

(iv) Put (ax+b)=t so that a dx = dt.

∴∫ax+b−−−−−√ dt=1a∫t√ dt=23at3/2+C=2(ax+b)3/23a+C.