The problems about Integrate Using u-Substitution

Problem	Solution
Integrate Using u-Substitution integral of 1/((8x…	Solution: Step 1 Define $u$ as $8 x - 1$ . Consequently, differentiate $u$ with respect to $x$ t…
Integrate Using u-Substitution integral of (sin(x…	Solution: Step 1: Choose $u = \cos (x)$ . Consequently, we have $d u = - \sin (x) d x$ , which im…
Integrate Using u-Substitution integral of e^(cos…	Solution: Step 1 Assign $u = \cos (x)$ . Consequently, $d u = - \sin (x) d x$ , which implies $-\f…
Integrate Using u-Substitution integral from 1 to…	Solution: Step 1 Choose $u = \frac{1}{x^{4}}$ . Consequently, we have $d u = - \frac{4}{x^…
Integrate Using u-Substitution integral of x/(1+x…	Solution: Step 1: Choose $u = 1 + x^{2}$ . Consequently, $d u = 2 x d x$ , which implies $\frac…
Integrate Using u-Substitution integral of (5x^2-…	Solution: Step 1: Reposition the constant $2$ in front of the expression $(5 x^{2} - 3)$ to…
Integrate Using u-Substitution integral of (4sin(…	Solution: Step 1: Define a new variable u Let $u = 3 + \cos (x)$ . This implies that $du = …
Integrate Using u-Substitution integral of sec(2x…	Solution: Step 1 Assign $u = \sec (2 x)$ . Consequently, $d u = 2 \sec (2 x) \tan (2 x) d x$ , which …
Integrate Using u-Substitution integral of (1+x)/…	Solution: Step 1: Decompose the integrand $\frac{1 + x}{1 + x^{2}}$ into two separate ter…
Integrate Using u-Substitution integral of sin(x)…	Solution: Step 1: Transform $\sin^{2} (x)$ using the half-angle identity to $\frac{1 - \cos…
Integrate Using u-Substitution integral of sin(x)…	Solution: Step 1: Transform $\sin^{2} (x)$ using the half-angle identity to $\frac{1 - \cos…
Integrate Using u-Substitution integral of x/( sq…	Solution: Step 1 Assign $u = x^{2} + 1$ . Then, calculate $d u = 2 x d x$ , which implies $\frac{…
Integrate Using u-Substitution integral of (x^2)/…	Solution: Step:1 Choose $u = 1 + x^{3}$ . Consequently, $d u = 3 x^{2} d x$ , which implies …
Integrate Using u-Substitution integral of (sin( …	Solution: Step:1 Implement exponent rules. Step:1.1 Express $\sqrt{x}$ as $x^{\frac…
Integrate Using u-Substitution integral of x squa…	Solution: Step:1 Choose $u = 1 - x^{2}$ . Then, differentiate to find $d u$ : $d u = - 2 x d x$ , …
Integrate Using u-Substitution integral of x squa…	Solution: Step:1 Choose $u = 4 - x^{2}$ . Consequently, $d u = - 2 x d x$ leads to $- \fra…
Integrate Using u-Substitution integral from 0 to…	Solution: Step:1 Define $u = 1 - x^{2}$ . Consequently, $d u = - 2 x d x$ implies $- \frac{…
Integrate Using u-Substitution integral of x/( sq…	Solution: Step:1 Choose $u = 1 - x^{2}$ . Consequently, we have $d u = - 2 x d x$ , which i…