Advertisements
Advertisements
प्रश्न
Advertisements
उत्तर
\[\int\left( 2^x + \frac{5}{x} - \frac{1}{x^\frac{1}{3}} \right)dx\]
\[ = \int 2^x dx + 5 \int\frac{dx}{x} - \int\frac{dx}{x^\frac{1}{3}}\]
\[ = \int 2^x dx + 5 \int\frac{dx}{x} - \int x^{- \frac{1}{3}} dx\]
\[ = \frac{2^x}{\ln 2} + 5 \ln x - \left[ \frac{x^{- \frac{1}{3} + 1}}{- \frac{1}{3} + 1} \right] + C\]
\[ = \frac{2^x}{\ln 2} + 5 \ln x - \frac{3}{2} x^\frac{2}{3} + C\]
APPEARS IN
संबंधित प्रश्न
\[\int\left\{ x^2 + e^{\log x}+ \left( \frac{e}{2} \right)^x \right\} dx\]
` ∫ {sec x "cosec " x}/{log ( tan x) }` dx
If \[\int\frac{\sin^8 x - \cos^8 x}{1 - 2 \sin^2 x \cos^2 x} dx\]
If `int(2x^(1/2))/(x^2) dx = k . 2^(1/x) + C`, then k is equal to ______.
The primitive of the function \[f\left( x \right) = \left( 1 - \frac{1}{x^2} \right) a^{x + \frac{1}{x}} , a > 0\text{ is}\]
\[\int\frac{1}{\sqrt{x} + \sqrt{x + 1}} \text{ dx }\]
\[\int\frac{1}{4 \sin^2 x + 4 \sin x \cos x + 5 \cos^2 x} \text{ dx }\]
