COMPASSLearning

Talk to us Register Login

CBSE Class 12 · 2008 · Indefinite IntegralsVery Short Answer

Evaluate :

\int \frac{x + c o s 6 x}{3 x ^{2} + s i n 6 x} d x

Answer: $\frac{1}{6} lo g 3 x^{2} + sin 6 x + C$

Solution

Put

t = 3 x^{2} + sin 6 x

, so

d t = (6 x + 6 cos 6 x) d x = 6 (x + cos 6 x) d x

, i.e.

(x + cos 6 x) d x = \frac{d t}{6}

. Then

\frac{1}{6} \int \frac{d t}{t} = \frac{1}{6} lo g ∣ t ∣ + C .

\frac{1}{6} lo g 3 x^{2} + sin 6 x + C

CBSE Class 12 Board · 2008 · Subjective

Practise more: all CBSE board PYQs on Indefinite Integrals →

More board questions on Indefinite Integrals

The integral $\int \frac{d x}{9 - 4 x ^{2}}$ is equal to
CBSE 2024View solution →
Find $\int cos^{3} x e^{l o g s i n x} d x$
CBSE 2024View solution →
Find $\int \frac{2 x + 1}{( x + 1 ) ^{2} ( x - 1 )} d x$
CBSE 2024View solution →
Anti-derivative of $\frac{tan x - 1}{tan x + 1}$ with respect to $x$ is:
CBSE 2023View solution →
Find $\int \frac{s i n ^{- 1} x}{( 1 - x ^{2} ) ^{3/2}} d x$
CBSE 2023View solution →
Evaluate $\int e^{x} (\frac{1 - s i n x}{1 - c o s x}) d x$
CBSE 2023View solution →