Evaluate e^ 3 _e x d x : - Vidyadip

Question

Evaluate $\int e^{3 \log _e x} d x$ :

✓

Answer

Let:
$
\begin{aligned}
I & =\int e^{3 \log _e x} d x \\
& =\int e^{\log _e x^3} d x=\int x^3 d x=\frac{1}{4} x^4+C
\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 "1 Marks" from Integrals→Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Integrate the function $\frac{1}{x \sqrt{a x-x^{2}}}$ [Hint: Put x = $\frac{a}{t}$]

Prove that $\cos ^ { - 1 } \left( \frac { 12 } { 13 } \right) + \sin ^ { - 1 } \left( \frac { 3 } { 5 } \right) = \sin ^ { - 1 } \left( \frac { 56 } { 65 } \right).$

Find a vector of magnitude $\sqrt{171}$ which is perpendicular to both of the vectors $\overrightarrow{\text{a}} = \hat{\text{i}} + 2\hat{\text{j}} - 3\hat{\text{k}}$ $\text{and} \overrightarrow{\text{b}} = 3\hat{\text{i}} - \hat{\text{j}} + 2\hat{\text{k}}.$

Let * be the binary operation on N given by a * b = L.C.M. of a and b. Find:

Find the identity of * in N

Integrate the function $f^{\prime}(a x+b)[f(a x+b)]^{n}$

The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x) = 0.005x³ - 0.02x² + 30x + 5000.
Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

Find all points of discontinuity of $\mathrm{f}$, where $\mathrm{f}$ is defined by: $f(x)=\left\{\begin{array}{l}\frac{|x|}{x}, \text { if } x \neq 0 \\ 0, \text { if } x=0\end{array}\right.$

Evaluate the following:
$\text{cosec}^{-1}\Big(\text{cosec}\frac{\pi}{4}\Big)$

Write the vector equation of the plane, passing through the point (a, b, c) and parallel to the plane $\overrightarrow{\text{r}}.(\hat{\text{i}} + \hat{\text{j}} + \hat{\text{k}}) = 2.$

If $3 \sin ^{-1} x+4 \cos ^{-1} x=2 \pi$, then find the value of $x$.