The problems about Integrate Using u-Substitution

Problem	Solution
Integrate Using u-Substitution integral of x^2 sq…	Solution: Step:1 Choose $u = x^{3} + 33$ . Consequently, $d u = 3 x^{2} d x$ . Express the i…
Integrate Using u-Substitution integral of (x+3)/…	Solution: Step:1 Choose $u = x^{2} + 6 x$ . Consequently, $d u = (2 x + 6) d x$ , which implies …
Integrate Using u-Substitution integral of (csc( …	Solution: Step 1: Rewrite the integral using exponent rules Step 1.1: Express $\sqrt{…
Integrate Using u-Substitution integral of 4(6x+1…	Solution: Step:1 Choose $u = 6 x + 1$ . Then differentiate to find $d u$ in terms of $d x$ . …
Integrate Using u-Substitution integral from 0 to…	Solution: Step 1: Choose a substitution variable Assign $u = 2 x$ . Compute the differential $du…
Integrate Using u-Substitution integral of (x^3+1…	Solution: Step:1 We recognize that u-substitution is not suitable for this integral. An al…
Integrate Using u-Substitution integral of 10x(5x…	Solution: Step 1 Assign $u = 5 x^{2} - 2$ . Compute $d u$ by differentiating $u$ with respect t…
Integrate Using u-Substitution integral of 6(1+6x…	Solution: Step 1: Choose $u = 1 + 6 x$ . Consequently, we have $d u = 6 d x$ , which implies $…
Integrate Using u-Substitution integral of 1/( sq…	Solution: Step 1 Assign $u = 5 x + 8$ . Consequently, $d u = 5 d x$ , which implies $\frac{1}{5}…
Integrate Using u-Substitution integral from 0 to…	Solution: Step 1: We cannot use u-substitution for this integral. We will employ a different …
Integrate Using u-Substitution integral of (x^3)/…	Solution: Step 1 Assign $u = 5 - \frac{1}{2} x^{4}$ . Compute the differential $d u$ . …
Integrate Using u-Substitution integral from 1 to…	Solution: Step:1 We cannot apply u-substitution to this integral. We will proceed with a…
Integrate Using u-Substitution integral of sin(x)…	Solution: Step 1 Assign $u = \cos (x)$ . Consequently, $d u = - \sin (x) d x$ , which implies $-\…
Integrate Using u-Substitution integral from 0 to…	Solution: Step 1: Identify that u-substitution is not applicable for this integral. We will …
Integrate Using u-Substitution integral of 28(7x-…	Solution: Step:1 Assign $u = 7 x - 2$ . Consequently, $d u = 7 d x$ , leading to the expression …
Integrate Using u-Substitution integral of x/(x+1…	Solution: Step:1 Choose $u = x + 1$ . Consequently, $d u = d x$ . Reformulate the integral in te…
Integrate Using u-Substitution integral of x^2sin…	Solution: Step 1 Assign $u = x^{3}$ . Consequently, $d u = 3 x^{2} d x$ , which implies $\frac{1}{…
Integrate Using u-Substitution integral of 1/(y s…	Solution: Step 1: We cannot use u-substitution to solve this integral. An alternative app…
Integrate Using u-Substitution integral of sin(x)…	Solution: Step 1: Extract $\cos^{2} (x)$ from the integral: $\int \sin^2(x) (\cos^2(x)\cos(…
Integrate Using u-Substitution integral of x squa…	Solution: Step 1 Choose $u = 1 + x$ and calculate $d u$ . Step 1.1 Set $u = 1 + x$ an…