# Important Questions for Class 12 Chapter 7 - Integrals

We have come up with CBSE important questions for class 12th chapter 7 Integrals with a lot of practice questions. A class 12th student clearly understands the importance of practicing any concept learned. Further, these list of questions are available for free. Download now!

**Important questions based on NCERT syllabus for Class 12 Chapter 7 - Integrals:**

*Question 1*: Integrate (8x+7) e^x

*Solution*: ∫(8x+7) e^x

Thsi equation of the form ∫u dv = u.v - ∫v du

Here u = 8x+ 7 dv = e^x

du = 8 v = ∫e^x

= e^x

∫u dv = u.v - ∫v du

∫(8x+7) e^x = e^x(8x+7) - ∫8e^x

= e^x(8x+7) - 8e^x + C where C is the integration constant.

*Question 2*: integrate ∫(1/xlogx) dx

*Solution*: Consider ∫(1/xlogx) dx

we add and subtract log in the numarator we get

∫(1 + log x - log x)/xlogx = ∫(1+log x)/xlog x - ∫logx/xlogx

= ∫(1+log x)/xlog x - ∫1/x dx

= ∫(1+log x)/xlog x - log|x| + C

Now we have to integrate (1+log x)/xlog x, for that we substitute

u = xlogx then du becomes x.1/x + logx(1) = 1 + logx

hence ∫(1+log x)/xlog x = ∫ du/u

= log|u| + C

= log|xlogx| + C

= log|x| + log|logx| + C

Therefore (1 + log x - log x)/xlogx = log|x| + log|logx| - log|x| + C

= log|logx| + C

*Question 3*: Integrate (e^(2x)-e^(-2x))/(e^(2x) + e^(-2x))

*Solution*: Let I = (e^(2x)-e^(-2x))/(e^(2x) + e^(-2x)).....(1)

Put e^(2x) + e^(-2x) = t

dt = 2e^(2x) - 2e^(-2x)

= 2(e^(2x) - e^(-2x))

dt/2 = e^(2x) - e^(-2x)

Substitute in equation 1 we get

I = ∫ (1/t) (dt/2)

= 1/2 ∫ dt/t

= 1/2(log|t|) + C

= 1/2(log(e^(2x) + e^(-2x)) + C