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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate : $\int e^{2x} \cos 5x dx$

$(a)\;\frac{e^{2x}}{2g}(2 \sin 5x + 5 \sin 5 x )+c \\(b)\;\frac{e^{2x}}{2g}(2 \cos 5x + 5 \sin 5 x )+c \\(c)\;\frac{e^{2x}}{2g}(2 \sin 5x + 5 \cos 5 x )+c \\ (d)\;None$
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$\int \large\frac{x^3 \sin ^{-1}(x^2)}{\sqrt {1-x^4}}$$dx$
By using formula :-
$\int e^{ax} \cos bx dx = \large\frac{e^{ax}}{a^2+b^2} $$(a \cos b x+ b \sin bx)$$+c$
Put $a=2; b=5$
$\large\frac{e^{2x}}{2g}$$(2 \cos 5x + 5 \sin 5 x )+c$
Hence b is the correct answer.
answered Jan 2, 2014 by meena.p
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