15.2 Indefinite Integral of Trigonometric Functions 三角函数的不定积分 - 独中课程 | 线上补习

高二数学 | 高级数学

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15.2 Indefinite Integral of Trigonometric Functions 三角函数的不定积分

Evaluate the following indefinite integral
求下列不定积分

*** QuickLaTeX cannot compile formula:
\int\of\begin\ sin\funcapply(\ 5x+1)dx〗

*** Error message:
Undefined control sequence \of.
leading text: $\int\of

Answer :

$-\frac{1}{5}cos(5x + 1) + C$

2) $\int\frac{dx}{{cos}^2{7}x}$

Answer :

$\frac{1}{7}tan7x + C$

3) $\int\frac{dx}{{sin}^2{(}2x+\frac{\pi}{4})}$

Answer :

$-\frac{1}{2}cot(2x + \frac{\pi}{4}) + C$

4) $\int{\frac{cos{x}}{{sin}^2{x}}dx}$

Answer :

–cosec x + C

5) $\int{\frac{cos{2}x}{cos{x}-sin{x}}dx}$

Answer :

sin x – cos x + C

6) $\int{{cos}^2{2}xdx}$

Answer :

$\frac{1}{2}x + \frac{1}{8}sin4x + C$

7) $\int{(1+2cos{x})^2dx}$

Answer :

3x + 4sin x + sin2x + C

8) $\int{\frac{1-{sin}^4{x}}{{sin}^2{x}}dx}$

Answer :

$-\cot{x-\frac{1}{2}x+\frac{1}{4}\sin{2x}+C}$

9) $\int{\frac{cos{2}x}{{sin}^4{x}}dx}$

Answer :

$\cot{x}-\frac{1}{3}\cot^3{x\ }+C$