1. Evaluate the following integrals: (a) Z(2 + 5x) sin(2x) dx (b) Zâ3/2^1/2 sinâ1 (y) dy 2. Evaluate each of the following integrals: (a) Z (ln(x)/x)^2 dx (b) Z e^6θ cos (e^3θ) dθ â Hint: Rewrite e^6θ = e^3θ ¡ e^3θ
Added by Tonte
Step 1
### 1. Evaluate the following integrals: #### (a) \(\int (2 + 5x) \sin(2x) \, dx\) ** Show moreâŚ
Show all steps
Close
Your feedback will help us improve your experience
Keondre Parker and 71 other Calculus 2 / BC educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Evaluate the integrals by making a substitution (possibly trigonometric) and then applying a reduction formula. $$\int_{0}^{\sqrt{3} / 2} \frac{d y}{\left(1-y^{2}\right)^{5 / 2}}$$
Techniques of Integration
Integral Tables and Computer Algebra Systems
Evaluate the following integrals: (a) ⍠x sin x dx (b) ⍠x cos 4x dx (c) ⍠xe^-x dx (d) ⍠x^2 cos x dx (e) ⍠2x^2 e^x dx (f) ⍠x^2 ln |x| dx (g) ⍠tan^-1 x dx (h) ⍠sin^-1 x dx (i) ⍠e^x cos x dx (j) ⍠sin^3 x dx Calculate the value of each of the following: (a) âŤ_0^Ď x cos 1/2 x dx (b) âŤ_0^1 x^2 e^x dx (c) âŤ_1^2 x^3 ln |x| dx (d) âŤ_0^Ď/4 x^2 sin 2x dx (e) âŤ_0^1 x tan^-1 x dx
Adi S.
Evaluate the following integrals. $$\int \frac{\sqrt{9 x^{2}-25}}{x^{3}} d x, x>\frac{5}{3}$$
Integration Techniques
Trigonometric Substitutions
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD