Google
Câu hỏi: Tìm họ các nguyên hàm của hàm số $f(x)=\dfrac{\sin \text{x}}{1+3\cos \text{x}}$
A. $\int{f(x)d\text{x}}=\ln \left| 1+3\cos \text{x} \right|+C$
B. $\int{f(x)d\text{x}}=3\ln \left| 1+3\cos \text{x} \right|+C$
C. $\int{f(x)d\text{x}}=-\dfrac{1}{3}\ln \left| 1+3\cos \text{x} \right|+C$
D. $\int{f(x)d\text{x}}=\dfrac{1}{3}\ln \left| 1+3\cos \text{x} \right|+C$
Ta có $\int{f(x)d\text{x}}=\int{\dfrac{\sin \text{x}}{1+3\cos \text{x}}dx=-\dfrac{1}{3}\int{\dfrac{d(1+3\cos \text{x})}{1+3\cos \text{x}}}}=-\dfrac{1}{3}\ln \left| 1+3\cos \text{x} \right|+C$.
A. $\int{f(x)d\text{x}}=\ln \left| 1+3\cos \text{x} \right|+C$
B. $\int{f(x)d\text{x}}=3\ln \left| 1+3\cos \text{x} \right|+C$
C. $\int{f(x)d\text{x}}=-\dfrac{1}{3}\ln \left| 1+3\cos \text{x} \right|+C$
D. $\int{f(x)d\text{x}}=\dfrac{1}{3}\ln \left| 1+3\cos \text{x} \right|+C$
Ta có $\int{f(x)d\text{x}}=\int{\dfrac{\sin \text{x}}{1+3\cos \text{x}}dx=-\dfrac{1}{3}\int{\dfrac{d(1+3\cos \text{x})}{1+3\cos \text{x}}}}=-\dfrac{1}{3}\ln \left| 1+3\cos \text{x} \right|+C$.
Đáp án C.