What Is u-Substitution?
Read this topicExplanations 5
- In this section, we'll learn about another technique for integration, called uuu-substitution. But before we start, let's look at a problem: The first two choices are technicall…
By Steven Kwon, Vedant Bonde, Victor Wang, Alex Federspiel
- We can take the derivative of a function by using the Chain Rule f(g(x))=f′(g(x))g′(x)f(g(x))=f'(g(x))g'(x)f(g(x))=f′(g(x))g′(x). The find the anti-derivative of a function with…
By Maya Schwartz, Moor Xu, Joshua Siktar
- Sometimes there are functions which cannot be integrated easily. ∫01(3t−1)5dx\int_0^1 (3t-1)^5 dx∫01(3t−1)5dx The integral above, for example, cannot be integrated in the curre…
By Lily Zacharias, Moor Xu
- (Video) Integration Using U-Substitution by PatrickJMT In this video by PatrickJMT he teaches how to use u-substitution in order to solve tricky integrals. U-substitution is a m…
By Alex Federspiel
- (Video) More Complicated Examples of U-Substitution by PatrickJMT In this video by patrickJMT he shows you how to solve some more complicated examples of integrals involving u-s…
By Alex Federspiel
Problems 10
- Let I=∫−1+12u332+u9981+u666duI = \int_{-1}^{+1} \frac{2u^{332} + u^{998}}{1 + u^{666}} duI=∫−1+11+u6662u332+u998du. Find 333I−π2333I - \frac{\pi}{2}333I−2π. Source: HMMT Febr…
- Compute ∫02x2cos(x3) dx\int_0^2 x^2 \cos(x^3) \, dx∫02x2cos(x3)dx.
- Compute ∫(2x+5)(x2+5x)8 dx\int (2x+5)(x^2+5x)^8 \, dx∫(2x+5)(x2+5x)8dx.
- Integrate ∫(4−x)61 dx\int (4-x)^{61} \, dx∫(4−x)61dx.
- Compute ∫01(3t−1)5 dt\int_0^1 (3t-1)^5 \, dt∫01(3t−1)5dt as a decimal to the nearest tenth.
- Integrate ∫(sint)1+cost dt\int (\sin t) \sqrt{1 + \cos t} \, dt∫(sint)1+costdt.
- Compute ∫ee41xlnx dx\int_e^{e^4} \frac1{x \sqrt{\ln x}} \, dx∫ee4xlnx1dx.
- Compute: 15∫03x+1−1 dx.15\int_{0}^{3}\sqrt{\sqrt{x+1} -1} \, dx.15∫03x+1−1dx. ASMT 2016 Guts Round #20
- Define the following function for x>0x\gt 0x>0: f(x)=∫1xdtt.f(x) = \int_{1}^{x}\frac{dt}{t}.f(x)=∫1xtdt. Which of the following is true?
- Solve ∫sinx1+cos2xdx\int\frac{\sin x}{1+\cos^2x}dx∫1+cos2xsinxdx