Home
Class 12
MATHS
Evaluate : (i) int(3x+5)^7dx (ii) int(4-...

Evaluate : (i) `int(3x+5)^7dx` (ii) `int(4-9x)^(5)dx` (iii) `int(1)/((2-3x)^(4))dx` (iv) `intsqrt(ax+b)\ dx`

Text Solution

Verified by Experts

(i) `"Put " (3x+5)="t so that "3dx=dt" or "dx=(1)/(3)dt`.
`:." "int(3x+5)^(7)dx=(1)/(3)t^(7)dt=(1)/(3)*(t^(8))/(8)+((3x+5)^(8))/(24)+C`.
(ii) Put `(4-9x)="t so that"-9dx=dtordx=-(1)/(9)dt`.
`:.int(4-9x)^(5)dx=-(1)/(9)int t^(5)dt=-(1)/(9)*(t^(6))/(6)+C(-(4-9x)^(6))/(54)+C`.
(iii) Put `(2-3x)="t so that"-3dx=dt" or "dx=-(1)/(3)dt`.
`:.int(1)/((2-3x)^(4))dx=-(1)/(3)int(1)/(t^(4))dt=-(1)/(3)*(1)/(-3t^(3))+C=(1)/(9(2-3x)^(3))+C`.
(iv) Put (ax+b)=t so that a dx = dt.
`:.intsqrt(ax+b)" dt"=(1)/(a)intsqrt(t)" dt"=(2)/(3a)t^(3//2)+C=(2(ax+b)^(3//2))/(3a)+C`.
Promotional Banner

Topper's Solved these Questions

  • METHODS OF INTEGRATION

    RS AGGARWAL|Exercise EXERCISE 13A VERY SHORT ANSWER QUESTIONS|10 Videos

  • METHODS OF INTEGRATION

    RS AGGARWAL|Exercise EXERCISE 13A SHORT ANSWER QUESTIONS|92 Videos

  • MATRICES

    RS AGGARWAL|Exercise Exercise 5F|21 Videos

  • PROBABILITY

    RS AGGARWAL|Exercise Exercise 29 B|2 Videos

Similar Questions

Explore conceptually related problems

(i) int(3x+5)^(4)dx

Evaluate: (i) int(1)/(4+9x^(2))dx (ii) int(1)/(9x^(2)-4)dx (iiii) int(1)/(16-9x^(2))dx

Evaluate: (i) int e^(2x-3)dx (ii) int a^(3x+2)dx

Evaluate : (i) intsqrt(9-x^(2))dx (ii) intsqrt(1-4x^(2))dx (iii) intsqrt(16-9x^(2))dx

Evaluate : (i) intcos2x\ dx (ii) inte^((5x+3))dx (iii) int sec^(2)(3x+5)dx (iv) intsin^(3)xdx

Evaluate : (i) int(dx)/((9x^(2)-1)) (ii) int(x)/((x^(4)-9))dx (iii) int(x^(2))/((x^(2)-9))dx

Evaluate: (i) int4x^(5)dx( ii) int2sin xdx (ii) int3^(x+2)dx (iv) int(1)/(2)sec^(2)xdx

Evaluate : (i) intx^(9)dx , (ii) int3sqrt(x) dx ,(iii) intdx (iv) int1/(x^(2))dx , (v) int(1)/(x^(1//3))dx , (vi) int5^(x) dx

Evaluate the following indefinite integrals : (i) intsqrt(a^(2)-x^(2))dx (ii) int(1)/(sqrt(49+x^(2)))dx (iii) int(1)/(xsqrt(x^(6)-1))dx (iv) intsqrt((1+x)/(1-x))dx (v) intsqrt((x^(2009))/(2x^(2008)-x^(2009)))dx (vi) int(1)/(sqrt((x-4)(x-5)))dx

Evaluate the following integrals : (i) int x^(15)dx (ii) int x^(-3//2)dx (iii) int(3x^(-7)+x^(-1))dx (iv) int(sqrt(x)+(1)/sqrt(x))^(2)dx (v) int(x+(1)/(x))dx (vi) int((a)/(x^(2))+(b)/(x))dx (a and b are constant)