Integration Worksheet3 solution1

In this page integration worksheet3 solution1 we are going to see solution of some practice question from the worksheet of integration.

Question 1

Integrate the following with respect to x ,5 x⁴ + 3 (2 x + 3)⁴ - 6 (4 - 3 x)⁵

Solution:

Now we are going to integrate the given function

     = ∫ 5 x⁴ + 3 (2 x + 3)⁴ - 6 (4 - 3 x)⁵ dx

     = ∫ 5 x⁴ dx + ∫ 3 (2 x + 3)⁴ dx - ∫ 6 (4 - 3 x)⁵ dx


Question 2

Integrate the following with respect to x,(3/x)+[m/(4x+1)]-2(5-2x)⁵

Solution:

Now we are going to integrate the given function

     = ∫(3/x)+[m/(4x+1)]-2(5-2x)⁵ dx

     = ∫ (3/x) dx + ∫ [m/(4x+1)] dx - ∫ 2(5-2x)⁵ dx

     = 3 ∫(1/x) dx + m ∫ [1/(4x+1)] dx - 2 ∫ (5-2x)⁵ dx

     = 3 log x + (m/4) log (4x+1)-2/(-2)(5-2x)^(5+1)/(5+1) + C

     = 3 log x + (m/4) log (4x+1)+ (5-2x)^6/6 + C


Question 3

Integrate the following with respect to x,  4 - 5/(x + 2) + 3 cos 2 x

Solution:

Now we are going to integrate the given function

     = ∫ 4 - 5/(x + 2) + 3 cos 2 x dx

     = 4∫ dx - 5 ∫ [1/(x+2)] dx + 3 ∫cos 2 x dx

     = 4 x - 5 log (x+2) + (3/2) sin 2 x + C


Question 4

Integrate the following with respect to x,3e^(7x)-4sec(4x+3)tan(4x+3)+11/x⁵

Solution:

Now we are going to integrate the given function

     = ∫  3 e^(7 x) - 4 sec (4 x + 3)tan (4x+3) + 11/x⁵ dx

     = 3 ∫ e^7x dx - 4 ∫ sec (4x+3)tan (4x+3) dx + 11 ∫ x^(-5) dx

     = 3 [e^7x/7] - 4 sec (4x+3)/4 + 11[x^(-5+1)/(-5+1)] + C

     = (3/7) e^7x - sec (4x+3) + 11[x^(-4)/(-4)] + C

     = (3/7) e^7x - sec (4x+3) - (11/4x⁴) + C


Question 5

Integrate the following with respect to x, pcosec²(px-q)-6(1-x)⁴+4e^(3-4x)

Solution:

Now we are going to integrate the given function

     = ∫pcosec²(px-q)-6(1-x)⁴+4e^(3-4x)dx

     = p ∫cosec²(px-q) dx - 6∫(1-x)⁴ dx + 4 ∫ e^(3-4x) dx

     = p [-cot (px-q)/p] - 6(1-x)^(4+1)/(4+1) + 4 e^(3-4x)/(-4) + C

     = -cot (px-q)- (6/5)(1-x)^5 -e^(3-4x) + C

integration worksheet3 solution1 integration worksheet3 solution1