Evaluate the following integrals: ^5x ^4xdx - Vidyadip

Question

Evaluate the following integrals:
$\int\tan^5\text{x }\sec^4\text{x}\text{dx}$

✓

Answer

$\int\tan^5\text{x }\sec^4\text{x}\text{dx}$
$=\int\tan^5\text{x }\sec^2\text{x}.\sec^2\text{x}\text{dx}$
$=\int\tan^5\text{x}(1+\tan^2\text{x})\sec^2\text{xdx}$
Let $\tan\text{x}=\text{t}$
$\sec^2\text{xdx}=\text{dt}$
Now, $\int\tan^5\text{x}(1+\tan^2\text{x})\sec^2\text{xdx}$
$=\int\text{t}^5(1+\text{t}^2)\text{dt}$
$=\int(\text{t}^5+\text{t}^7)\text{dt}$
$=\frac{\text{t}^6}{6}+\frac{\text{t}^8}{8}+\text{C}$
$=\frac{\tan^6\text{x}}{6}+\frac{\tan^8\text{x}}{8}+\text{C}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(3 Marks)" from Indefinite Integrals→Indefinite Integrals — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point 'c' in the indicated interval as stated by the Lagrange's mean value theorem.
$f(x) = 2x^2 - 3x + 1$ on $[1, 3]$

Show that the line through points $(1, -1, 2)$ and $(3, 4, -2)$ is perpendicular to the line throught the points (0, 3, 2) and $(3, 5, 6).$

State the converse, inverse and contrapositive of the conditional statement : 'If a sequence is bounded, then it is convergent'.

Each of the total five questions in a multiple choice examination has four choices, only one of which is correct. A student is attempting to guess the answer. The random variable $x$ is the number of questions answered correctly. What is the probability that the student will give atleast one correct answer ?

$\int_0^{\pi / 2} \frac{\cos X}{(1+\sin x)(2+\sin x)} \cdot d x$

Evaluate the following integrals:$\int\frac{1}{\sqrt{8+3\text{x}-\text{x}^2}}\text{ dx}$

If $\text{y}=\frac{\log\text{x}}{\text{x}},$ show that $\frac{\text{d}^2\text{y}}{\text{dx}^2}=\frac{2\log\text{x}-3}{\text{x}^3}.$

Solve the differential equation, $d r+(2 r \cot \theta+\sin 2 \theta) d \theta=0$.

Find the angle between planes $\bar{r} \cdot(\hat{i}+\hat{j}+2 \hat{k})=13$ and $\bar{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=31$.

Evaluate the following:

$\int x^2 \sin 3 x d x$