微積分學/不定積分/練習

1. $\int {\frac {3x}{2}}dx$…………答案：${\frac {3}{4}}x^{2}+C$
2. 求$f(x)=2x^{4}$的原函數…………答案：${\frac {2x^{5}}{5}}+C$
3. $\int (7x^{2}+3\cos x-e^{x})dx$…………答案：${\frac {7x^{3}}{3}}+3\sin x-e^{x}+C$
4. $\int ({\frac {2}{5x}}+\sin x)dx$…………答案：${\tfrac {2}{5}}\ln |x|-\cos x+C$
5. $\int x\sin 2x^{2}dx$…………答案：$-{\frac {\cos 2x^{2}}{4}}+C$
6. $\int -3e^{\sin x}\cos xdx$…………答案：$-3e^{\sin x}+C$
7. $\int {\frac {2x-5}{x^{3}}}dx$…………答案：${\frac {5-4x}{2x^{2}}}+C$
8. $\int (2x-1)e^{-3x+1}dx$…………答案：${\frac {(1-6x)e^{1-3x}}{9}}+C$

解答

例題

$\int \tan ^{4}x\sec ^{6}xdx$