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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 55

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 55

Answers (1)

Answer: \frac{1}{6}\log \left | 3x^{2}+\sin 6x \right |+c

Hints: You must know about the integral rule of trigonometric functions.

Given: \int \frac{x+\cos 6x}{3x^{2}+\sin6x}dx

Solution:

\int \frac{x+\cos 6x}{3x^{2}+\sin6x}dx

Let    3x^{2}+\sin 6x=t     and differentiate both sides,\left [ \frac{d}{dx}\sin x=\cos x \right ]

(6x+6\cos 6x)dx=dt

(x+\cos 6x)dx=\frac{dt}{6}

\begin{aligned} &I=\int \frac{d t}{6 t}=>\frac{1}{6} \log (t)+c \\ &=\frac{1}{6} \log \left|3 x^{2}+\sin 6 x\right|+c \quad\quad\quad\quad\quad\left[\int \frac{1}{x} d x=\log x+c\right]\\ \end{aligned}

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