Problem 856
\(\displaystyle \int{\dx\over x+5}=? \qquad\qquad \int \sqrt[3]{1-3x}\dx=? \qquad\qquad \int (e^{-x}+e^{-2x+3})\dx=? \) Difficulty: 1. |
Problem 857
\(\displaystyle \int{\dx\over 5+4x^2}=? \qquad\qquad \int\Big({1-x\over x}\Big)^2\dx=? \qquad\qquad \int\left(1-{1\over x^2}\right)\sqrt{x\sqrt{x}}\dx=? \) Difficulty: 2. |
Problem 858
\(\displaystyle \int xe^{-x} \dx=? \qquad\qquad \int x^2\log x \dx=? \qquad\qquad \int \th^2 x \dx=? \) Difficulty: 3. |
Problem 859
\(\displaystyle \int \sqrt{1-t^2} \dt=? \qquad\qquad \int \sqrt{1+x^2}\dx=? \qquad\qquad \int {\dx\over \sin x}=? \) Difficulty: 4. |
Problem 861
\(\displaystyle \int {4x^5-5x^4+16x^3-19x^2+12x-16 \over (x-2)^2(x^4+4x^2+4)} \dx=? \) Difficulty: 4. |
Problem 862
\(\displaystyle \int {x^5+4x^4+12x^3+14x^2+15x+12 \over (x+2)(x^2+3)}\dx=? \) Difficulty: 4. |
Problem 863
\(\displaystyle \int {x^2 \over \sqrt{1+x+x^2}}\dx=? \) Difficulty: 4. |
Problem 867
\(\displaystyle \int{\dx\over 1+\sqrt{1-2x-x^2}}=?\) Difficulty: 4. |
Problem 868
Let \(\displaystyle a,b\in \R\). \(\displaystyle \int{\dx\over a\sin x +b \cos x}=?\) Difficulty: 4. |
Problem 860
\(\displaystyle \int |x|\dx=? \qquad\qquad \int |x^2-1|\dx=? \qquad\qquad \int {\sqrt{1+x^2}+\sqrt{1-x^2}\over \sqrt{1-x^4}}\dx=? \) Difficulty: 5. |
Problem 864
\(\displaystyle \int \sqrt{x^3+x^4}\dx=? \) Difficulty: 5. |
Problem 865
\(\displaystyle \int {x-\sqrt{x^2+3x+2} \over x+\sqrt{x^2+3x+2}}\dx=? \) Difficulty: 5. |
Problem 866
\(\displaystyle \int \sin x\cdot \log(\tg x)\dx=? \) Difficulty: 5. |
Supported by the Higher Education Restructuring Fund allocated to ELTE by the Hungarian Government |