6. S dx 6x+1

Q: V3 (b) x V5x2 +1 dx. (Hint: be smart.)

A: We need to find the value of ∫03x35x2+1dx

Q: 12 dr r3 – I

A:

Q: dx 4. 4+ 3Vx

A: To solve∫x4+3xdx

Q: How would I evaluate this indefinite integral?

A: Consider the provided indefinite integral,Simplify the given indefinite integral as follows,

Q: 9. 3. dx Vx-1 X – 1 4

A:

Q: Find the integral. ∫ ( (3 / x 3 ) + ( 2 / x ) + ( 4 / x 4 ) dx.

A:

Q: +3 х2-5х, dx

A: ∫x3+3x2-5xx dx

Q: Find the integral. Show complete solution. x+4 dx X-4 1.

A: ∫x+4x-4dx

Q: S(4x – 1)dx

A: ∫4x-1 dx

Q: dx S x²(x²+x+1) √ √ex - 1dx

A:

Q: Compute the given integral. 16dx +C

A:

Q: fa |(1 + 63*(6) ds 25 – x² (– 2x) dx

A:

Q: 3. 9. dx 4 -1

A: We have to evaluate the integral.

Q: 2- Vx dx (x + 1)²

A: Given:             ∫2-xx+12dx Expand: 2-xx+12dx=2x+12-xx+12 Apply the sum rule: ∫fx±gxdx=∫fxdx±∫gxdx…

Q: 2x S x5 e ²x dx

A:

Q: Evaluate the integral: | x(24 – x)7/2 dx

A:

Q: (4+lnx)5

A:

Q: „(2x+3)dx x²+3x

A: ∫2x+3 dxx2+3x Put, x2+3x=tDifferentiating with respect to x, we get⇒2x+31=dtdx⇒2x+3 dx=dt

Q: [(7x-2)e-* dx; -3x

A: The given question can be solved as shown in step2.

Q: ex 4-9e²x dx

A:

Q: 1 2 (x+1)² dx

A:

Q: Use substitution to find the indefinite integral. 2 | 5z² – 3 dz -3 dz =

A: Given: I=∫z5z2-3dz   ...1   As we know the Power rule: ∫xndx=xn+1n+1+C

Q: evaluate the integral.

A:

Q: Evaluate the integrals

A: 59. ∫0∞x2e-xdx60. ∫0∞xe3xdx

Q: | x(8 + 4x°) dx = + C.

A: Indefinite Integration

Q: Evaluate the integral: x(19 – x)3/2 dx = %3D

A: Given: ∫x(19-x)32dx

Q: 2x -dx 2 x + 2x + 5

A:

Q: xe*dx .3.

A:

Q: x' +4x + 3 dx x* + 5.x? + 4

A:

Q: ) dx 5.

A: the given integral is: ∫1x-2+1x dx we have to evaluate the given integral.   let the given integral…

Q: SE + 8) dx 3. 4

A: Given: 3.∫x24+8dx4.∫x2 3+1xdx

Q: 1. dy y3 2. S(6 - x) (4 + x)dx

A:

Q: 1 + ) dx 4.

A: The given integral is ∫x23+1x dx. Evaluate the above integral as follows.

Q: 36* -dx V 6* + 3

A:

Q: 2(x*) dx

A:

Q: What change of variables would you use for the integral  ∫(4 - 7x)-6 dx?

A: Consider the following integral: I=∫4-7x-6dx Substitute 4-7x=t→-7dx=dt→dx=-17dt in I:…

Q: 1 x²e dx = 1 2. %3D 2T 10- I

A: First we use symmetry of even function then we let x2 /2=u then using laplace transform.

Q: x3 + 4 dx. (Be smart.) x2 +1

A: By integration, we have

Q: ヤ -3 x4 – 4x2 + 13 dx

A: SOLUTION-

Q: dx x+2 17.

A: There are multiple question. As per Company policy ask other question separately. 17.

Q: ds 1. S- (4s?-24s+27)2 3

A:

Q: x³ + 3x dx. x2 + 1

A:

Q: (5x³+ 3x²-8' 10. S )dx x2

A: 10) The given integral ∫5x3+3x2-8x2dx can be evaluated as, ∫5x3+3x2-8x2dx=∫5x3x2+3x2x2-8x2dx…

Q: Please find the value of integral in the image.

A: It is given that

Q: 1. (х + 2)? dx х— 2

A:

Q: Evaluate the double integrals: [[(x + y+1)dxdy

A:

Q: S(2 - ) dz 4.

A: ∫z-14 dz

Q: Use a change of variables or the table to evaluate the following indefinite integral. 2x2 dx 13-4x

A: Given,          ∫2x23-4x3dx

Q: dr 4.

A:

Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.