5.4: Substitution

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May 15, 2024
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- 5.3: The Fundamental Theorem of Calculus
- 5.5: Integrals Involving Exponential and Logarithmic Functions

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Evaluate $\displaystyle \int (x+1)^4\ dx$ .
Evaluate $\displaystyle \int \dfrac{1}{(2x - 3)^7}\ dx$ .
Evaluate $\displaystyle \int x(x^2+3)^{100}\ dx$ .
Evaluate $\displaystyle \int \dfrac{1}{\sqrt{1 - 5t}}\ dx$ .
Evaluate $\displaystyle \int x\sqrt{2x^2 + 3}\ dx$ .
Evaluate $\displaystyle \int \dfrac{x}{\sqrt{1 - x^2}}\ dx$ .
Evaluate $\displaystyle \int x\sin(x^2)\ dx$ .
Evaluate $\displaystyle \int \cos^3 \theta \sin \theta\ d\theta$ .
Evaluate $\displaystyle \int t\sin(t^2)\cos(t^2)\ dt$ .
Evaluate $\displaystyle \int x^3\sqrt{1 - x^2}\ dx$ .
Evaluate $\displaystyle \int \dfrac{y^5}{(1-y^3)^{3/2}}\ dy$ .
Evaluate $\displaystyle \int_0^1 2(1 - x)^7\ dx$ .
Evaluate $\displaystyle \int_{-1}^2 x(1 - x^2)^3\ dx$ .
Evaluate $\displaystyle \int_{-1}^2 (2x + 3)\sqrt[3]{x^2 + 3x - 1} dx$ .
Evaluate $\displaystyle \int_{0}^{\pi} \sin^5(3x)\cos(3x)\ dx$ .
Evaluate $\displaystyle \int_{0}^{\sqrt{\pi}/2} x\sec^2(x^2)\tan(x^2)\ dx$ .
Evaluate $\displaystyle \int_{0}^1 \dfrac{t^2}{\sqrt{1 + t^3}} \ dt$ .
Evaluate $\displaystyle \int_{-1}^1 \dfrac{y^3}{(1 + y^2)^3}\ dx$ .
Evaluate $\displaystyle \int_{\pi/4}^{\pi/3} \sec^2 \theta \tan \theta\ d\theta$ .

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