Evalute : x^3 1+x^4 d x - Vidyadip

Question

Evalute : $\int \frac{x^3}{\sqrt{1+x^4}} d x$

✓

Answer

Let $I=\int \frac{x^3}{\sqrt{1+x^4}} d x$
Put $1+x^4=t \quad \therefore 4 x^3 d x=d t$
$
\begin{aligned}
& \therefore x^3 d x=\frac{d t}{4} \\
& \begin{aligned}
\therefore I & =\int \frac{1}{\sqrt{t}} \cdot \frac{d t}{4}=\frac{1}{4} \int t^{-\frac{1}{2}} d t \\
& =\frac{1}{4} \cdot \frac{t^{\frac{1}{2}}}{\left(\frac{1}{2}\right)}+c \\
& =\frac{1}{2} \sqrt{1+x^4}+c .
\end{aligned}
\end{aligned}
$

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.(2 Marks)" from Integration (p-1)→Integration (p-1) — all question types→Maths (commerce) STD 12 Commerce / Arts question papers→Maharashtra Board STD 12 Commerce / Arts question papers→Maharashtra Board question paper generator→

Similar questions

Find the present value of an annuity immediate of $\text{₹} 36,000$ p.a. for 3 years at $9 \%$ p.a. compounded annually. [Given: $\left.(1.09)^{-3}=0.7722\right]$

Find $\frac{d y}{d x}$ if, :
$
x^3+y^3+4 x^3 y=0
$

Find the differential equation whose general solution is $x^3+y^3=$ 35ax.

Evalute : $\int e^{\sqrt{x}} d x$

Solve the following differential equations : $\frac{d y}{d x}=x^2 y+y$

Prepare the truth tables for the following statement patterns : p → (~p ∨ q)

Let X represent the difference between a number of heads and the number of tails obtained when a coin is tossed 6 times. What are the possible values of X?

Find the number of years for which an annuity of $\text{₹}$ $500$ is paid at the end of every years, if the accumulated amount works out to be $\text{₹}$ $1,655$ when interest is compounded annually at $10 \%$ p.a

Write the converse, inverse, contrapositive of the following statements :
If a man is a bachelor, then he is happy.

Check whether following matrices are invertible or not: $\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 4 & 5 \\ 2 & 4 & 6\end{array}\right]$