Question

Find ∫(11x 3

+10x 2
−5x+4)dx ∫(11x 3
+10x 2
−5x+4)dx= 4
11
​
x 4
+ 3
10
​
x 3
− 2
5
​
x 2
+4x+C

Answer 1

Step-Let's find the integral of the expression ∫(11x^3 + 10x^2 - 5x + 4)dx step by step:

∫(11x^3 + 10x^2 - 5x + 4)dx

First, let's find the integral of each term separately:

∫(11x^3)dx = (11/4)x^4 + C1, where C1 is the constant of integration.

∫(10x^2)dx = (10/3)x^3 + C2, where C2 is the constant of integration.

∫(-5x)dx = (-5/2)x^2 + C3, where C3 is the constant of integration.

∫(4)dx = 4x + C4, where C4 is the constant of integration.

Now, we can add these integrals together:

(11/4)x^4 + C1 + (10/3)x^3 + C2 + (-5/2)x^2 + C3 + 4x + C4

Combine the constants of integration:

C1 + C2 + C3 + C4 = C

So, the final result is:

(11/4)x^4 + (10/3)x^3 - (5/2)x^2 + 4x + Cby-step explanation: