不定积分$\int
\tan ^{2}x \sec^{2}x\text{d}x=$( )
A: $\frac{1}{3}{{\tan }^{3}}x+C$
B: $-\frac{1}{3}{{\tan }^{3}}x+C$
C: $\frac{1}{3}{{\sec }^{3}}x+C$
D: $-\frac{1}{3}{{\sec }^{3}}x+C$
\tan ^{2}x \sec^{2}x\text{d}x=$( )
A: $\frac{1}{3}{{\tan }^{3}}x+C$
B: $-\frac{1}{3}{{\tan }^{3}}x+C$
C: $\frac{1}{3}{{\sec }^{3}}x+C$
D: $-\frac{1}{3}{{\sec }^{3}}x+C$
举一反三
- 不定积分$\int<br/>\tan ^{3}x \sec x\text{d}x=$( ) A: $\frac{1}{3} \sec^3 x+\sec x+C$ B: $\frac{1}{3} \sec^3 x-\sec x+C$ C: $\sec^3 x-\sec x+C$ D: $\sec^3 x+\sec x+C$
- \(\int { { {\tan }^{10}}x { { \sec }^{2}}xdx}\)=( ) A: \(-\frac{1}{11} { { \tan }^{11}}x+C\) B: \(\frac{1}{11} { { \tan }^{11}}x+C\) C: \(\frac{1}{11} { { \cot }^{11}}x+C\) D: \(-\frac{1}{11} { { \cot }^{11}}x+C\)
- \(\int { { {\sec }^{3}}xdx}\)=( ) A: \(\frac{1}{2}\sec x\cot x-\frac{1}{2}\ln \left| \sec x+\tan x \right|+C\) B: \(\frac{1}{2}\sec x\tan x+\frac{1}{2}\ln \left| \sec x+\tan x \right|+C\) C: \(-\frac{1}{2}\csc x\tan x+\frac{1}{2}\ln \left| \sec x-\cot x \right|+C\) D: \(-\frac{1}{2}\sec x\tan x-\frac{1}{2}\ln \left| \csc x+\tan x \right|+C\)
- \(\int { { {\sin }^{2}}x { { \cos }^{5}}xdx}\)=( ) A: \(\frac{1}{3} { { \sin }^{3}}x-\frac{2}{5} { { \sin }^{5}}x+\frac{1}{7} { { \sin }^{7}}x+C\) B: \(\frac{2}{3} { { \sin }^{3}}x-\frac{1}{5} { { \sin }^{5}}x-\frac{1}{7} { { \sin }^{7}}x+C\) C: \(\frac{1}{3} { { \cos }^{3}}x-\frac{2}{5} { { \cos }^{5}}x+\frac{1}{7} { { \cos }^{7}}x+C\) D: \(\frac{2}{3} { { \cos }^{3}}x-\frac{1}{5} { { \cos }^{5}}x-\frac{1}{7} { { \cos }^{7}}x+C\)
- 微分方程$y' = \sqrt{x},y(1)=0$的解为 A: $ \frac{2}{3} x^{\frac{3}{2}} + C $ B: $ \frac{2}{3} x^{\frac{3}{2}} -\frac{2}{3} $ C: $ x^{\frac{3}{2}}-1 $ D: $ x^{\frac{3}{2}}+C $