CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Integration by Parts

Evaluate: ∫ ...

Question

Evaluate:

$\int e^{x^{3} + x^{2} - 1} (3 x^{4} + 2 x^{3} + 2 x) d x$

Open in App

Solution

$\int e^{x^{3} + x^{2} - 1} (3 x^{4} + 2 x^{3} + 2 x) d x$
Notice that $(x^{3} + x^{2} - 1) = 3 x^{2} + 2 x$ that $3 x^{4} + 2 x^{3} = x^{2} (3 x^{2} + 2 x)$
$(3 x^{4} + 2 x^{3} + 2 x) e^{x^{3} + x^{2} - 1} = x^{2} (3 x^{2} + 2 x) e^{x^{3} + x^{2} - 1} + 2 x e^{x^{3} + x^{2} - 1}$
$= x^{2} (x^{3} + x^{2} - 1)^{1} e^{x^{3}} + x^{2} - 1 + (x^{2})^{1} e^{x^{3} + x^{2} - 1}$
$= x^{2} (e^{x^{3} + x^{2} - 1}) + (n^{2})^{1} e^{x^{3}} + x^{2} = 1$
$= (x^{2} e^{x^{3} + x^{2} - 1})^{1}$
Now, $\int (x^{2} e^{x^{3} + x^{2} - 1})^{1} d x$
$= x^{2} e^{x^{3} + x^{2} - 1} + C$

Suggest Corrections

thumbs-up

0

Similar questions

\int_{0}^{2} (x^{2} + e^{- 2 x}) d x

\int \frac{1 - x^{2}}{x (1 - 2 x)} d x

.

\int \frac{1 - x^{2}}{x (1 - 2 x)} d x

Q. Evaluate the integrals

\int_{1}^{2} \frac{1}{(x^{2} + 2 x)} d x

lim x \to 2 \frac{x^{3} - 8}{x^{2} - 4}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Integration by Parts

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Integration by Parts

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon