Find the following integral- -2 x3-3 sin x-5 -x d x

∫ (2x^3 3 sin x+5 √(x))dx =2 ∫ x^2 dx 3 ∫ sin x dx +5 ∫ x^1/2dx =2x^3/3 3 ( cos x)+5x^(1/2)+1/(1/2)+1+C =2/3x^3+3 cos x +5 × 2/3x^3/2+C =2/3x^3+3 cos x+10/3x ...

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Byju's Answer

Standard XII

Mathematics

Property 1

Find the foll...

Question

Find the following integral.
$\int (2 x^{3} - 3 s i n x + 5 \sqrt{x}) d x .$

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Solution

$\int (2 x^{3} - 3 s i n x + 5 \sqrt{x}) d x = 2 \int x^{2} d x - 3 \int s i n x d x + 5 \int x^{\frac{1}{2}} d x = \frac{2 x^{3}}{3} - 3 (- c o s x) + 5 \frac{x^{(\frac{1}{2}) + 1}}{(\frac{1}{2}) + 1} + C = \frac{2}{3} x^{3} + 3 c o s x + \frac{5 \times 2}{3} x^{\frac{3}{2}} + C = \frac{2}{3} x^{3} + 3 c o s x + \frac{10}{3} x^{\frac{3}{2}} + C$

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Similar questions

Q. Find the integral of

\int (2 x^{2} - 3 sin x + 5 \sqrt{x}) d x

\int (2 x^{2} - 3 sin x + 5 \sqrt{x}) d x

is equal to (where

C

is the constant of integration)

\int (2 x^{2} - 3 s i n x + 5 \sqrt{x}) d x

Find the following integrals.
$\int \frac{2 - 3 s i n x}{c o s^{2} x} d x .$

\int \frac{2 x^{3} - 1}{x^{4} + x} d x

is equal to
(where

C

is constant of integration)

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Find the following integral. ∫(2x3−3sinx+5√x)dx.

∫(2x3−3sinx+5√x)dx=2∫x2dx−3∫sinxdx+5∫x12dx=2x33−3(−cosx)+5x(12)+1(12)+1+C=23x3+3cosx+5×23x32+C=23x3+3cosx+103x32+C

Find the following integral.
$\int (2 x^{3} - 3 s i n x + 5 \sqrt{x}) d x .$